Translations of Logical Formulas and the Equiconsistency Problem
Andrei A. Kuzichev · Mathematical logic quarterly · 1994
Abstract A translation of formulas in a language L1 to formulas in a language L2 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 L1 to theories in L2. 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 L1 such that its inclusion in a theory T (in L1) guarantees equiconsistency of F and F(T), then we propose axiomatizations of A(F) for some F's. Mathematics Subject Classification: 03B10, 03B15, 03F25.