Some preservation theorems in an intermediate logic. (English) Zbl 1100.03014

Bagheri, Seyed M.

Math. Log. Q. 52, No. 2, 125-133 (2006).

The author presents first steps in the model theory of a logic intermediate betweeen intuitionistic and classical logic, called semi-classical logic, in which \(x=y \vee x\neq y\) is an axiom. Models for semi-classical theories are special kinds of Kripke models whose frame is a linear order. Beside the usual notion of submodel, there are notions of left and right submodels, and thus of left and right model completeness. A theory turns out to be left (right) model-complete if and only if every formula is equivalent under \(T\) to an existential (universal) one. Similar preservation theorems are proved for left and right inductive theories.

Reviewer: Victor V. Pambuccian (Phoenix)

MSC:

03B55	Intermediate logics
03C40	Interpolation, preservation, definability

Keywords:

semi-classical logic; preservation theorems; Kripke models; inductive theories; model completeness

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