of a preordered set ( A , ≤ ) {\displaystyle (A,\leq )} is said to be cofinal or frequent in A {\displaystyle A} if for every a ∈ A , {\displaystyle...

especially in order theory, the cofinality cf(A) of a partially ordered set A is the least of the cardinalities of the cofinal subsets of A. Formally, cf ⁡...

below, C, remained the lower limit. In addition to the range, the tenor (cofinal, or dominant, corresponding to the "reciting tone" of the psalm tones)...

Cofinal may refer to: Cofinal (mathematics), the property of a subset B of a preordered set A such that for every element of A there is a "larger element"...

h ( I ) {\displaystyle h(I)} is cofinal in A . {\displaystyle A.} The set h ( I ) {\displaystyle h(I)} being cofinal in A {\displaystyle A} means that...

The cofinality of any ordinal α is a regular ordinal, i.e. the cofinality of the cofinality of α is the same as the cofinality of α. So the cofinality operation...

mathematical theory, introduced by Saharon Shelah (1978), that deals with the cofinality of the ultraproducts of ordered sets. It gives strong upper bounds on...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

Archimedean property is related to the concept of cofinality. A set X contained in an ordered set F is cofinal in F if for every y in F there is an x in X such...

indexed by ℶ {\displaystyle \beth } . On the other hand, beth numbers are cofinal (every cardinal number is less than a beth number) in plain Zermelo-Fraenkel...

a final map. Also, a map f : X → Y {\displaystyle f:X\to Y} is called cofinal if f : X o p → Y o p {\displaystyle f:X^{op}\to Y^{op}} is final. Presheaf...

consequence of the axiom of choice, the principle that every total order has a cofinal well-order, can be combined to prove the full axiom of choice. With these...

into itself then α {\displaystyle \alpha } is either a limit ordinal of cofinality ω {\displaystyle \omega } or the successor of such an ordinal. The axioms...

{\displaystyle Q} of a partially ordered set P {\displaystyle P} is said to be cofinal if for every x ∈ P {\displaystyle x\in P} there exists some y ∈ Q {\displaystyle...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

cardinals with cofinality ℵ 0 {\displaystyle \aleph _{0}} . An uncountably infinite cardinal κ {\displaystyle \kappa } having cofinality ℵ 0 {\displaystyle...

x_{\bullet }=\left(x_{a}\right)_{a\in A}} is said to be frequently or cofinally in S {\displaystyle S} if for every a ∈ A {\displaystyle a\in A} there...

theory, the notion of final functor is a generalization of the notion of cofinal set from order theory. A functor F : C → D {\displaystyle F:C\to D} is...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

isomorphism) in this way as the lattice of lower sets of a unique finite poset. Cofinal set – a subset U {\displaystyle U} of a partially ordered set ( X , ≤ )...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

{\displaystyle \kappa <\operatorname {cf} (2^{\kappa })} (where cf(α) is the cofinality of α) and if  κ < λ  then  2 κ ≤ 2 λ . {\displaystyle {\text{if }}\kappa...

an initial subsequence of the cf(κ)-sequence. Thus its cofinality is less than the cofinality of κ and greater than it at the same time; which is a contradiction...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

E_{j}} suspends to an (i + 1)-cell in E j + 1 {\displaystyle E_{j+1}} , a cofinal subspectrum is a subspectrum for which each cell of the parent spectrum...

theory, a regular cardinal is a cardinal number that is equal to its own cofinality. More explicitly, this means that κ {\displaystyle \kappa } is a regular...

the theorem. Kőnig's theorem has also important consequences for the cofinality of cardinal numbers. If κ ≥ ℵ 0 {\displaystyle \kappa \geq \aleph _{0}}...

-1}^{\aleph _{\alpha }}.} This formula was, together with a later notion called cofinality introduced by Hausdorff, the basis for all further results for Aleph exponentiation...

disproof and established Kőnig's theorem, which by using the concept of cofinality introduced in 1908 by Felix Hausdorff, shows that result that 2 ℵ 0 {\displaystyle...

Euclidean distance. A class of ordinal numbers is said to be unbounded, or cofinal, when given any ordinal, there is always some element of the class greater...

set). Let κ {\displaystyle \kappa \,} be a limit ordinal of uncountable cofinality λ . {\displaystyle \lambda .} For some α < λ {\displaystyle \alpha <\lambda...

In set theory, a mathematical discipline, a fundamental sequence is a cofinal sequence of ordinals all below a given limit ordinal. Depending on author...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

{\displaystyle x} if and only if B {\displaystyle {\mathcal {B}}} is a cofinal subset of ( N ( x ) , ⊇ ) {\displaystyle \left({\mathcal {N}}(x),\supseteq...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

the whole set. Subsets that are unbounded in the whole set. A subset is cofinal in the whole set if and only if it is unbounded in the whole set or it...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

indiscernible, all of them must have cofinality ω in the forcing extension. Thus the proto-Silver ordinals all have cofinality ω in the forcing extension, even...

superior and limit inferior Irreducible element Prime element Compact element Cofinal and coinitial set, sometimes also called dense Meet-dense set and join-dense...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

_{2}} to an ordinal of cofinality ω {\displaystyle \omega } . Let G {\displaystyle G} be an ω {\displaystyle \omega } -sequence cofinal on ω 2 L {\displaystyle...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

following statement: 2cf(κ) < κ implies κcf(κ) = κ+, where cf denotes the cofinality function. Note that κcf(κ)= 2κ for all singular strong limit cardinals...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

_{\alpha }(\beta )<\delta } ). The fundamental sequence for an ordinal with cofinality ω is a distinguished strictly increasing ω-sequence that has the ordinal...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

D {\displaystyle C\subset D} be exact categories. Then C is said to be cofinal in D if (i) it is closed under extension in D and if (ii) for each object...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

quotient L / Z, where L is a linearly ordered group and Z is a cyclic cofinal subgroup of L. Every cyclically ordered group can also be expressed as...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

dense subsets. If P is a non-empty upwards ccc poset and Y is a set of cofinal subsets of P with |Y| ≤ κ then there is an upwards-directed set A such...

case where μ is counting measure. Given an ordinal a with uncountable cofinality, a subset of a is called a club if it is closed in the order topology...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

is either empty or Prikry generic over K (so it has order type ω and is cofinal in κ) and unique except up to a finite initial segment. If K has no inaccessible...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

This implies that V and V[G] have the same cardinals (and the same cofinalities). A subset D of P is called dense if for every p ∈ P there is some q...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

MS16. Malliaris, M.; Shelah, S. (2016), "Cofinality spectrum theorems in model theory, set theory, and general topology", Journal of the American Mathematical...

not equivalent; in fact, the smallest worldly cardinal has countable cofinality and therefore is a singular cardinal. The following are in strictly increasing...

\left\langle A_{\delta }:\delta \in S\right\rangle } such that every Aδ is a cofinal subset of δ for every unbounded subset A ⊆ κ {\displaystyle A\subseteq...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

class of ordinal numbers, and because O n {\textstyle \mathbb {On} } is cofinal in N o {\textstyle \mathbb {No} } we have { N o ∣ } = { O n ∣ } = O n {\textstyle...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

numbers. If λ {\displaystyle \lambda } is an ordinal number of uncountable cofinality, the nonstationary ideal on λ {\displaystyle \lambda } is the collection...

all left-hand Riemann sums and the set of all right-hand Riemann sums is cofinal in the set of all tagged partitions. Another popular restriction is the...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

a powerset. If κ {\displaystyle \kappa } is a cardinal of uncountable cofinality, S ⊆ κ , {\displaystyle S\subseteq \kappa ,} and S {\displaystyle S} intersects...

with the order topology. These continuous functions are often used in cofinalities and cardinal numbers. A normal function is a function that is both continuous...

}\times A)\times _{B^{\mathrm {op} }\times B}\operatorname {Tw} (B),} are cofinal. Cisinski, Denis-Charles (2019-06-30). Higher Categories and Homotopical...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

{\displaystyle \vert \mathbb {R} \vert >\aleph _{0}} ⁠, and a limit on its cofinality (roughly, how difficult it is to approach ⁠ c {\displaystyle {\mathfrak...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

that are in infinitely many of these sets (or equivalently, that are in cofinally many of them). That is, x ∈ lim sup n → ∞ A n {\displaystyle x\in \limsup...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

Archimedean fields in terms of these substructures. The natural numbers are cofinal in K {\displaystyle K} . That is, every element of K {\displaystyle K}...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

\kappa \mapsto \kappa ^{\mathrm {cf} (\kappa )}} where cf denotes the cofinality function; the gimel function is used for studying the continuum function...

cases, equality can be ruled out by König's theorem on the grounds of cofinality (e.g. c ≠ ℵ ω {\displaystyle {\mathfrak {c}}\neq \aleph _{\omega }} )...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

Problem", Silver proved that if a cardinal κ is singular with uncountable cofinality and 2λ = λ+ for all infinite cardinals λ < κ, then 2κ = κ+. Prior to Silver's...

κcf(κ) and κ < cf(2κ) for any infinite cardinal κ, where cf(κ) is the cofinality of κ. Assuming the axiom of choice and, given an infinite cardinal κ and...

\ldots \}=\bigcup _{n<\omega }\beth _{n}} is a strong limit cardinal of cofinality ω. More generally, given any ordinal α, the cardinal ℶ α + ω = ⋃ n < ω...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

etc. The classes of successor ordinals and limit ordinals (of various cofinalities) as well as zero exhaust the entire class of ordinals, so these cases...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

multiples of p r . {\displaystyle p_{r}.} If H {\displaystyle H} is a cofinal sequence (that is, any normal subgroup of finite index contains some H...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

existed in the San Isidro-Tarna area. The Republicans advanced through the Cofiñal valley, conquering the Sierra de Rebollares and the opposite bank. They...

has an upper bound. Since every totally ordered set has a well-ordered cofinal subset, this is equivalent to saying that the preordered set is the opposite...

group theory, semigroups, and cofinality in universal algebra. Her final publication, published posthumously, was "Cofinality of algebras" (1986).[F] During...

{\displaystyle {\mathcal {P}}(\kappa )\,} . We also have that this sequence is cofinal in the order defined, i.e. every member of P ( κ ) {\displaystyle {\mathcal...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

of I {\displaystyle I} are cofinal with the symbolic powers of I {\displaystyle I} . This important property of being cofinal was further developed by Schenzel...

I {\displaystyle h:A\to I} such that h ( A ) {\displaystyle h(A)} is a cofinal subset of I {\displaystyle I} . Thus, f ( x ∙ ) {\displaystyle f\left(x_{\bullet...

everywhere Almost never Almost surely Analytic capacity Closed unbounded set Cofinal (mathematics) Cofinite Dense set IP set 2-large Large set (Ramsey theory)...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

{\displaystyle +} , this definition is equivalent to the one given above. Cofinal (mathematics) Cofiniteness Ergodic Ramsey theory Piecewise syndetic set...

cardinal characteristics. Stephen Hechler. On the existence of certain cofinal subsets of ω ω {\displaystyle {}^{\omega }\omega } . In T. Jech (ed), Axiomatic...

in J(c). Consequently, J(c) is also a distributive lattice, and it is cofinal in Sieve(c). Artin, Michael; Alexandre Grothendieck; Jean-Louis Verdier...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

follows from 2κ = κ+ for stationary S that do not contain ordinals of cofinality κ. Shelah showed that the diamond principle solves the Whitehead problem...

nonstandard, as then the (infinite) collection of y {\displaystyle y} could be cofinal in M {\displaystyle {\mathcal {M}}} . The following relations hold between...

of some regular cardinal κ ≥ ω2 and every element of S has countable cofinality, then there is an ordinal α < κ such that S ∩ α is stationary in α. In...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

Partition regularity Regular cardinal, a cardinal number that is equal to its cofinality Regular modal logic Regular conditional probability, a concept that has...

of the positive cone C {\displaystyle C} of X {\displaystyle X} that is cofinal in C {\displaystyle C} (e.g. H {\displaystyle H} could be C {\displaystyle...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

represents the special case where the direct system of compact subsets has a cofinal sequence. The set of ends of any compact space is the empty set. The real...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

fundamental sequence for an ordinal number α {\displaystyle \alpha } with cofinality cof ⁡ ( α ) = β {\displaystyle \operatorname {cof} (\alpha )=\beta } is...

case holds for cardinals of the form λ = κω, but not for cardinals λ of cofinality ω (because λ < λcof λ). A complete first-order theory T is called totally...

{\displaystyle \{\beta _{\gamma }\}_{\gamma <\mathrm {cf} \,(\alpha )}} cofinal in α {\displaystyle \alpha } with β 0 = 0 {\displaystyle \beta _{0}=0}...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

set cofinal A subset of a poset is called cofinal if every element of the poset is at most some element of the subset. cof cofinality cofinality 1.  The...

female bus driver. She went on to establish the first bus line between Cofiñal and Boñar, which she had initially established in 1908 using a horse-drawn...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

closed and unbounded subset of κ, so that for every λ in C of uncountable cofinality, there is an unbounded subset of λ that is homogenous for f; slightly...

ordinals below the Bachmann–Howard ordinal (which are all of countable cofinality), we might define standard sequences converging to any one of them (provided...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

is categorical in a cardinal λ {\displaystyle \lambda } of high-enough cofinality, then tameness holds for types over saturated models of size less than...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

sequential spaces, Fréchet–Urysohn spaces are exactly those for which a "cofinal convergent diagonal sequence" can always be found, similar to the diagonal...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

A\in I(\exists B\in {\mathcal {B}})(A\subseteq B)\}.} The "cofinality" of I is the cofinality of the partial order (I, ⊆). It is easy to see that we must...

forcing with any generic set over such an order preserves cardinals and cofinalities. Furthermore, the ccc property is preserved by finite support iterations...

Arrow property". arXiv:math/0112213. Malliaris, M.; Shelah, S. (2016). "Cofinality spectrum theorems in model theory, set theory, and general topology"....

intersects A i {\displaystyle A_{i}} for all i {\displaystyle i} in a cofinal subset of I {\displaystyle I} . When these sets agree, the common set is...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

Jackson, Stephen C. (1999), "The calculus of partition sequences, changing cofinalities, and a question of Woodin", Transactions of the American Mathematical...

Power Function over singular cardinals. Gitik, Moti (1986). "Changing Cofinalities and the Nonstationary Ideal". Israel Journal of Mathematics. 56 (3):...

ordinal definable disjoint stationary subsets of κ made of ordinals of cofinality ω. The consistency strength of the determinacy hypothesis is unknown but...

phenomenon. For any ordered group L and any central element z that generates a cofinal subgroup Z of L, the quotient group L / Z is a cyclically ordered group...

I)(\exists A\in {\mathcal {A}})(B\subseteq A){\big \}}.} The "cofinality" of I is the cofinality of the partial order (I, ⊆). It is easy to see that we must...

of the power set of ω is ℵ α {\displaystyle \aleph _{\alpha }} if the cofinality of ℵ α {\displaystyle \aleph _{\alpha }} is not ω; otherwise, its cardinality...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

of forcing. He generalized the Prikry forcing in order to change the cofinality of a large cardinal to a predetermined regular cardinal. He proved that...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

vector lattice Banach Fréchet Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet...

either 0, an even successor ordinal, or a limit ordinal of countable cofinality. Similar notions of reduction and degree arise by replacing the continuous...