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Bounded finite set theory
Mathematical Logic Quarterly 67 (2):149-163 (2021)
Abstract
We define an axiom schema for finite set theory with bounded induction on sets, analogous to the theory of bounded arithmetic,, and use some of its basic model theory to establish some independence results for various axioms of set theory over. Then we ask: given a model M of, is there a model of whose ordinal arithmetic is isomorphic to M? We show that the answer is yes if.Other Versions
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References found in this work
On Interpretations of Arithmetic and Set Theory.Richard Kaye & Tin Lok Wong - 2007 - Notre Dame Journal of Formal Logic 48 (4):497-510.
A Mathematical Introduction to Logic.Herbert Enderton - 2001 - Bulletin of Symbolic Logic 9 (3):406-407.
Metamathematics of First-Order Arithmetic.Petr Hajék & Pavel Pudlák - 1994 - Studia Logica 53 (3):465-466.
Induction and foundation in the theory of hereditarily finite sets.Flavio Previale - 1994 - Archive for Mathematical Logic 33 (3):213-241.
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