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Fragments of Kripke–Platek set theory and the metamathematics of $$\alpha $$ α -recursion theory

Sy-David Friedman, Wei Li & Tin Lok Wong

Archive for Mathematical Logic 55 (7-8):899-924 (2016)

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Initial self-embeddings of models of set theory.Ali Enayat & Zachiri Mckenzie - 2021 - Journal of Symbolic Logic 86 (4):1584-1611.details By a classical theorem of Harvey Friedman, every countable nonstandard model $\mathcal {M}$ of a sufficiently strong fragment of ZF has a proper rank-initial self-embedding j, i.e., j is a self-embedding of $\mathcal {M}$ such that $j[\mathcal {M}]\subsetneq \mathcal {M}$, and the ordinal rank of each member of $j[\mathcal {M}]$ is less than the ordinal rank of each element of $\mathcal {M}\setminus j[\mathcal {M}]$. Here, we investigate the larger family of proper initial-embeddings j of models $\mathcal {M}$ of fragments of (...) Download Export citation Bookmark
On the relative strengths of fragments of collection.Zachiri McKenzie - 2019 - Mathematical Logic Quarterly 65 (1):80-94.details Let be the basic set theory that consists of the axioms of extensionality, emptyset, pair, union, powerset, infinity, transitive containment, Δ0‐separation and set foundation. This paper studies the relative strength of set theories obtained by adding fragments of the set‐theoretic collection scheme to. We focus on two common parameterisations of the collection: ‐collection, which is the usual collection scheme restricted to ‐formulae, and strong ‐collection, which is equivalent to ‐collection plus ‐separation. The main result of this paper shows that for (...) Download Export citation Bookmark 2 citations
End extending models of set theory via power admissible covers.Zachiri McKenzie & Ali Enayat - 2022 - Annals of Pure and Applied Logic 173 (8):103132.details Download Export citation Bookmark

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