# Normal Form for Deductions in Predicate Calculus with Equality and Functional Symbols

## Abstract

It is known how useful an apparatus the G. Gentzen [1] fundamental theorem turns out to be in investigations concerning predicate calculus. The plan of a finite proof of the possibility of extending the fundamental theorem to predicate calculus with equality and functional symbols is proposed herein. In the course of the proof we shall establish several theorems on specialization of the form of the deduction in some sequential versions of the predicate calculus with equality and functional symbols which are free of sections. In themselves, these results turn out to be useful for the proof of a number of assertions connected with the predicate calculus with equality and functional symbols.

## Keywords

Fundamental Theorem Elementary Sequence Atomic Formula Structural Rule Sequential Version## Preview

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## Literature Cited

- 1.Gentzen, G., “Untersuchungen über das logische Schliessen. I,” Math. Z, 39(2):176–210 (1934).Google Scholar
- 2.Kanger, S., “A simplified proof method for elementary logic,” in: Computer Programming and Formal Systems. Studies in Logic, 1963, pp. 87–94.CrossRefGoogle Scholar