FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
1998, VOLUME 4, NUMBER 2, PAGES 733-749
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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Last modified: June 17, 1998