Nonaxiomatizability results for infinitary systems
- 9 October 1967
- journal article
- Published by Cambridge University Press (CUP) in The Journal of Symbolic Logic
- Vol. 32 (3) , 367-384
- https://doi.org/10.2307/2270780
Abstract
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.Keywords
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