FPM 1998, vol. 4, no. 2, pp. 733-749

FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(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 $$ \mathcal L(T)
$$ 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.

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