(FUNDAMENTAL AND APPLIED MATHEMATICS)

1998, VOLUME 4, NUMBER 2, PAGES 733-749

## Decidable first order logics

R. E. Yavorsky

Abstract

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The logic $\mathcal L\left(T\right)$ 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 $\mathcal L\left(T\right)$ 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 $\mathcal L\left(T\right)$ turn out to be undecidable.

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