Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 50, Number 3 (2009), 227-244.
Finitary Set Theory
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.
Notre Dame J. Formal Logic, Volume 50, Number 3 (2009), 227-244.
First available in Project Euclid: 13 November 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 03C13: Finite structures [See also 68Q15, 68Q19] 03D20: Recursive functions and relations, subrecursive hierarchies 03E10: Ordinal and cardinal numbers 03E30: Axiomatics of classical set theory and its fragments
Kirby, Laurence. Finitary Set Theory. Notre Dame J. Formal Logic 50 (2009), no. 3, 227--244. doi:10.1215/00294527-2009-009. https://projecteuclid.org/euclid.ndjfl/1257862036