FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1999, VOLUME 5, NUMBER 1, PAGES 221-255

V. E. Plisko

Abstract

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It is proved in this paper that the predicate logic of each complete
constructive arithmetic theory
```$T$ having the existence property is
$\Pi_1^T$ -complete. In this connection the techniques
of uniform partial
truth definition for intuitionistic arithmetic theories is used.
The main theorem is applied to the characterization of the predicate logic
corresponding to certain variant of the notion of realizable predicate
formula. Namely it is shown that the set of undisprovable predicate
formulas is recursively isomorphic to the complement
of the set $\emptyset^{(\omega +1)}$ .

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Last modified: April 27, 1999