Stage comparison, fixed points, and least fixed points in Kripke-Platek environments

DOI10.1215/00294527-2022-0025OpenAlexW4311896049MaRDI QIDQ2108575

Yanyan Li

Publication date: 19 December 2022

Published in: Notre Dame Journal of Formal Logic (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-63/issue-4/Stage-Comparison-Fixed-Points-and-Least-Fixed-Points-in-KripkePlatek/10.1215/00294527-2022-0025.full

zbMATH Keywords

Kripke-Platek set theoryfixed points and least fixed points of monotone operatorsstage comparison theorem

Mathematics Subject Classification ID

Axiomatics of classical set theory and its fragments (03E30) Proof theory in general (including proof-theoretic semantics) (03F03) Inductive definability (03D70)

Cites Work

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• A new model construction by making a detour via intuitionistic theories. I: Operational set theory without choice is \(\Pi_1\)-equivalent to KP
• Elementary induction on abstract structures
• Full and hat inductive definitions are equivalent in NBG
• From Mathesis Universalis to Fixed Points and Related Set-Theoretic Concepts
• ABOUT SOME FIXED POINT AXIOMS AND RELATED PRINCIPLES IN KRIPKE–PLATEK ENVIRONMENTS