FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2002, VOLUME 8, NUMBER 3, PAGES 783-828

**The elements of the constructive model theory**

V. E. Plisko

Abstract

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A generalized predicate is defined as a function from the
natural numbers $$**N**
to $2$**N**.
The values of a generalized predicate are treated as "the
realizations" of sentences.
The logical operations on the generalized predicates are based on the
ideas of Kleene's recursive realizability.
A generalized algebraic system is defined on the ground of the
concept of a generalized predicate.
The notions of constructive truth in an enumerated system and in an
arbitrary denumerable system are defined.
It is shown that the relations of logical consequence corresponding to
these semantics have not the compactness property and the set of
logical tautologies is $$P_{1}^{1}-complete.
The problems of axiomatizing the classes of algebraic systems in the
languages with constructive semantics are studied.

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published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/k02/k023/k02312h.htm

Last modified: February 17, 2003