Finitary Set Theory

Notre Dame Journal of Formal Logic 50 (3):227-244 (2009)
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Abstract

I argue for the use of the adjunction operator (adding a single new element to an existing set) as a basis for building a finitary set theory. It allows a simplified axiomatization for the first-order theory of hereditarily finite sets based on an induction schema and a rigorous characterization of the primitive recursive set functions. The latter leads to a primitive recursive presentation of arithmetical operations on finite sets

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Citations of this work

Addition and multiplication of sets.Laurence Kirby - 2007 - Mathematical Logic Quarterly 53 (1):52-65.
Gödel on Deduction.Kosta Došen & Miloš Adžić - 2019 - Studia Logica 107 (1):31-51.
A hierarchy of hereditarily finite sets.Laurence Kirby - 2008 - Archive for Mathematical Logic 47 (2):143-157.

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References found in this work

Finitism.W. W. Tait - 1981 - Journal of Philosophy 78 (9):524-546.
On Interpretations of Arithmetic and Set Theory.Richard Kaye & Tin Lok Wong - 2007 - Notre Dame Journal of Formal Logic 48 (4):497-510.
On n-quantifier induction.Charles Parsons - 1972 - Journal of Symbolic Logic 37 (3):466-482.
On 퐧-Quantifier Induction.Charles Parsons - 1972 - Journal of Symbolic Logic 37 (3):466 - 482.
Saturated models of universal theories.Jeremy Avigad - 2002 - Annals of Pure and Applied Logic 118 (3):219-234.

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