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AXIOMS FOR FINITE COLLAPSE MODELS OF ARITHMETIC

Published online by Cambridge University Press:  18 November 2014

ANDREW TEDDER
ANDREW TEDDER*
Affiliation:
University of Connecticut
*
*UNIVERSITY OF CONNECTICUT USA E-mail: [email protected]
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Abstract

The collapse models of arithmetic are inconsistent, nontrivial models obtained from ℕ and set out in the Logic of Paradox (LP). They are given a general treatment by Priest (Priest, 2000). Finite collapse models are decidable, and thus axiomatizable, because finite. LP, however, is ill-suited to normal axiomatic reasoning, as it invalidates Modus Ponens, and almost all other usual conditional inferences. I set out a logic, A3, first given by Avron (Avron, 1991), and give a first order axiom system for the finite collapse models. I present some standard arithmetical axioms in addition to a cyclic axiom and prove that these axioms are sound and complete for the cyclic models, reporting a similar result for the heap models. The state of the situation for the each of the kinds of infinite collapse model is, however, left an open question.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 8 , Issue 3 , September 2015 , pp. 529 - 539
Copyright
Copyright © Association for Symbolic Logic 2014 

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