Journal of Mathematical Sciences

, Volume 87, Issue 1, pp 3234–3252

# A method of epsilon substitution for the predicate logic with equality

• G. E. Mints
Article

## Abstract

The method of epsilon substitution was defined for arithmetic with interpretation of αxA(x) as the least x satisfying A(x). It proceeds by a series of finite approximations “from below” to a solution of a fixed system of critical formulas. For the predicate logic only approach “from above” similar to cut-elimination was available. We present a definition of epsilon substitution for the predicate logic, prove the termination of the substitution process, and derive the corresponding Herbrand-type theorem. Bibliography: 18 titles.

### Keywords

Predicate Logic Fixed System Substitution Process Finite Approximation Critical Formula

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