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.
Citation
Laurence Kirby. "Finitary Set Theory." Notre Dame J. Formal Logic 50 (3) 227 - 244, 2009. https://doi.org/10.1215/00294527-2009-009
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