Arithmetic complexity of the predicate logics of complete arithmetic theories

Valeri Plisko

pp. 57-66

in: Artur Rojszczak, Jacek Cachro, Gabriel Kurczewski (eds), Philosophical dimensions of logic and science, Berlin, Springer, 2003

Abstract

It seems that the most natural problem in mathematical logic is studying the logics of mathematical theories. If the logics of first-order theories are considered, the situation can be formalized in the following way. Let T be a first-order theory, i.e. a set of closed formulas in a first-order language L. A closed predicate formula is called T-valid if each its closed L-instance is in T. We denote the set of T-valid predicate formulas by L(T) and call it the predicate logic of the theory T.