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Nonaxiomatizability results for infinitary systems

Published online by Cambridge University Press:  12 March 2014

Carol Karp
Carol Karp*
Affiliation:
University of Maryland
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Extract

Methods are being developed for treating questions of decidability in fewer than Ω steps, Ω being a regular nondenumerable cardinal. In this paper we consider the set-theoretical predicate Taut(x), “x is a tautology,” taken in the infinitary sense. In case x is hereditarily finite there is no question that it is decidable in finitely many steps. But what if x is infinite? We are not assuming that x is in any way constructive or even that the propositional formulas can be well-ordered, so it is not appropriate to treat this predicate as one of natural numbers or even as one of ordinals.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 32 , Issue 3 , 09 October 1967 , pp. 367 - 384
Copyright
Copyright © Association for Symbolic Logic 1967

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