Talk:Projective determinacy
Article states that PD is undecidable in ZFC, but as far as I know (and consulting the references given) it is merely unknown whether it is consistent with ZFC
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 | On 11 May 2025, it was proposed that this article be moved from Axiom of projective determinacy to Projective determinacy. The result of the discussion was moved. |
Independence
Article states that PD is undecidable in ZFC, but as far as I know (and consulting the references given) it is merely unknown whether it is consistent with ZFC (but most mathematicians think it is). Don't have a reference to hand on this, though. Fish-Face (talk) 21:36, 3 May 2011 (UTC)
- Depends on what you mean by "known". ZFC+PD has strictly higher consistency strength than ZFC, and therefore it is impossible to prove in ZFC that PD is consistent. (Unless, of course, ZFC is inconsistent, in which case ZFC does prove that ZFC+PD is consistent, and ZFC proves everything else as well).
- But it's misleading to say that it's "unknown". It's "known" in the same sense that, say, ZFC itself is "known" to be consistent, or even something like Peano arithmetic is "known" to be consistent. It's not a matter of proof, because that gets you into an infinite regress where you have to justify the reliability of the proof system first. It's more of an empirical fact. --Trovatore (talk) 21:59, 3 May 2011 (UTC)
- And still, the phrase "The axiom is independent of ZFC (assuming that it is consistent with ZFC), unlike the full axiom of determinacy (AD), which contradicts the Axiom of Choice" looks strange for me. PD does not follow from ZFC (and hopefully does not contradict it); AD does contradict (and hopefully does not follow...). The "unlike" is a bit misleading, and "independent (assuming consistency)" is hardly more clear than just "does not follow from" (or "is not a theorem of"). Boris Tsirelson (talk) 12:15, 17 December 2012 (UTC)
Requested move 11 May 2025
- The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.
The result of the move request was: moved. Moved as an uncontested request with minimal participation. If there is any objection within a reasonable time frame, please ask me to reopen the discussion; if I am not available, please ask at the technical requests page. (closed by non-admin page mover) Jeffrey34555 (talk) 17:39, 25 May 2025 (UTC)
Axiom of projective determinacy → Projective determinacy – PD is a proposition about set theory. It could be taken as an axiom; it could be proved from other axioms; it could be treated as an open question; in some contexts (say in L) it could even be mentioned as a false assertion. There is no obvious reason to emphasize the axiomatic status, particularly given that it has been proved from large cardinals. Trovatore (talk) 20:44, 11 May 2025 (UTC) — Relisting. Jeffrey34555 (talk) 00:35, 19 May 2025 (UTC)
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