Translations of Logical Formulas and the Equiconsistency Problem | Zendy

Kuzichev Andrei A. | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

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.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research