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Countable inductive definitions in AST. (English) Zbl 0614.03053
In the paper the author adapts some ideas from the research of inductive definitions for the alternative set theory (AST). For understanding the paper the reader must have relatively deep knowledge in both areas (AST and inductive definitions). An interesting result is that $$\Sigma$$- classes coincide with the inductive ones. The investigation of positive formulas (being used in AST in a larger scale for the first time) appears to be useful. Let us mention, e.g., one result not yet published: $$\Sigma$$ I-classes introduced by the author (a generalization of $$\Sigma$$-classes for a general cut I) are identical with those defined from I by positive formulas.
Reviewer: K.Čuda
##### MSC:
 3e+70 Nonclassical and second-order set theories
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