Bounded finite set theory | Zendy

Kirby Laurence | Zendy

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Bounded finite set theory

Author(s) -

Kirby Laurence

Publication year - 2021

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/malq.202000056

Subject(s) - mathematics , bounded function , axiom , schema (genetic algorithms) , set theory , model theory , finite set , zermelo–fraenkel set theory , discrete mathematics , independence (probability theory) , axiom of choice , set (abstract data type) , algebra over a field , pure mathematics , computer science , mathematical analysis , statistics , geometry , machine learning , programming language

We define an axiom schema I Δ 0 S for finite set theory with bounded induction on sets, analogous to the theory of bounded arithmetic, I Δ 0 , and use some of its basic model theory to establish some independence results for various axioms of set theory over I Δ 0 S . Then we ask: given a model M of I Δ 0 , is there a model of I Δ 0 S whose ordinal arithmetic is isomorphic to M ? We show that the answer is yes if M ⊧ Exp .

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