A hierarchy of hereditarily finite sets

Archive for Mathematical Logic 47 (2):143-157 (2008)
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Abstract

This article defines a hierarchy on the hereditarily finite sets which reflects the way sets are built up from the empty set by repeated adjunction, the addition to an already existing set of a single new element drawn from the already existing sets. The structure of the lowest levels of this hierarchy is examined, and some results are obtained about the cardinalities of levels of the hierarchy

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10.1007/s00153-008-0073-7

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Citations of this work

Finitary Set Theory.Laurence Kirby - 2009 - Notre Dame Journal of Formal Logic 50 (3):227-244.
Addition and multiplication of sets.Laurence Kirby - 2007 - Mathematical Logic Quarterly 53 (1):52-65.
Ordinal operations on graph representations of sets.Laurence Kirby - 2013 - Mathematical Logic Quarterly 59 (1-2):19-26.
Substandard models of finite set theory.Laurence Kirby - 2010 - Mathematical Logic Quarterly 56 (6):631-642.
Digraph parameters and finite set arithmetic.Laurence Kirby - 2015 - Mathematical Logic Quarterly 61 (4-5):250-262.

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References found in this work

Finitism.W. W. Tait - 1981 - Journal of Philosophy 78 (9):524-546.
Inner models for set theory—Part I.J. C. Shepherdson - 1951 - Journal of Symbolic Logic 16 (3):161-190.
Slim models of zermelo set theory.A. R. D. Mathias - 2001 - Journal of Symbolic Logic 66 (2):487-496.
Finitary Set Theory.Laurence Kirby - 2009 - Notre Dame Journal of Formal Logic 50 (3):227-244.

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