ZFC PROVES THAT THE CLASS OF ORDINALS IS NOT WEAKLY COMPACT FOR DEFINABLE CLASSES

DOI10.1017/JSL.2017.75zbMath1447.03016arXiv1610.02729OpenAlexW2963610041WikidataQ129898451 ScholiaQ129898451MaRDI QIDQ4638982

Joel David Hamkins, Ali Enayat

Publication date: 2 May 2018

Published in: The Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.02729

zbMATH Keywords

Zermelo-Fraenkel set theoryweakly compact cardinalGödel-Bernays class theory

Mathematics Subject Classification ID

Consistency and independence results (03E35) Large cardinals (03E55) Models of arithmetic and set theory (03C62)

Related Items (3)

Set theory with a proper class of indiscernibles ⋮ First‐order undefinability of the notion of transfinitely uplifting cardinals ⋮ Rank-initial embeddings of non-standard models of set theory

Uses Software

• MathOverflow

Cites Work

• Set theory. An introduction to independence proofs. 2nd print
• Blunt and topless end extensions of models of set theory
• On Certain Elementary Extensions of Models of Set Theory
• Power-like models of set theory
• On the consistency of the Definable Tree Property on ℵ₁
• Powers of regular cardinals
• Ramsey's theorem and recursion theory
• Some impredicative definitions in the axiomatic set theory
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