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Translations of Logical Formulas and the Equiconsistency Problem
Author(s) -
Kuzichev Andrei A.
Publication year - 1994
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19940400107
Subject(s) - mathematics , prefix , translation (biology) , substitution (logic) , transformation (genetics) , subject (documents) , propositional calculus , mathematics subject classification , algebra over a field , discrete mathematics , pure mathematics , linguistics , computer science , philosophy , biochemistry , chemistry , messenger rna , library science , gene
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.