This article is cited in 2 papers

Decidable first order logics

R. È. Yavorskii

M. V. Lomonosov Moscow State University

Abstract: The logic $\mathcal L(T)$ of arbitrary first order theory $T$ is the set of predicate formulae, provable in $T$ under every interpretation into the language of $T$. It is proved, that for the theory of equation and the theory of dense linear order without minimal and maximal elements $\mathcal L(T)$ is decidable, but can not be axiomatized by any set of schemes with restricted arity. On the other hand, for most of the expressively strong theories $\mathcal L(T)$ turn out to be undecidable.

UDC: 510.6

Received: 01.10.1996

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