Natural Number Arithmetic in the Theory of Finite Sets

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dc.creatorMayberry, J. P.
dc.creatorPettigrew, Richard
dc.date2007-11-19
dc.date2008-08-08
dc.date.accessioned2026-07-07T09:55:16Z
dc.date.available2026-07-07T09:55:16Z
dc.descriptionWe describe a theory of finite sets, and investigate the analogue of Dedekind's theory of natural number systems (simply infinite systems) in this theory. Unlike the infinitary case, in our theory, natural number systems come in differing lengths and with different closure properties. We give examples of natural number systems incomparable in length; we define hierarchies of natural number systems closed under increasingly powerful functions; and we describe a method by which to construct natural number systems with given closure properties. These natural number systems form natural models for various systems of weak arithmetic.
dc.description53 pages; second version; section 6 added; section 12 revised; material added on connection with bounded arithmetic
dc.identifierhttps://arxiv.org/abs/0711.2922
dc.identifierhttp://arxiv.org/abs/0711.2922
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/166566
dc.subjectLogic
dc.subject03C62
dc.titleNatural Number Arithmetic in the Theory of Finite Sets
dc.typetext

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