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Translations of Logical Formulas and the Equiconsistency Problem

โœ Scribed by Andrei A. Kuzichev

Publisher
John Wiley and Sons
Year
1994
Tongue
English
Weight
369 KB
Volume
40
Category
Article
ISSN
0044-3050

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โœฆ Synopsis

Abstract

A translation of formulas in a language L~1~ to formulas in a language L~2~ is a mapping which preserves the parameters and commutes with the substitution prefix, the propositional connectives and the quantifiers. Every translation generates a corresponding transformation of theories in L~1~ to theories in L~2~. We formulate the equiconsistency problem for such transformations and propose a variant of its solution. First, for a transformation F we find the least theory A(F) in L~1~ such that its inclusion in a theory T (in L~1~) guarantees equiconsistency of F and F(T), then we propose axiomatizations of A(F) for some F's.

Mathematics Subject Classification: 03B10, 03B15, 03F25.

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