Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990 Association of Mizar Users

## A Classical First Order Language

Czeslaw Bylinski
Warsaw University, Bialystok
Supported by RPBP.III-24.C1.

### Summary.

The aim is to construct a language for the classical predicate calculus. The language is defined as a subset of the language constructed in [7]. Well-formed formulas of this language are defined and some usual connectives and quantifiers of [7], [1] are accordingly. We prove inductive and definitional schemes for formulas of our language. Substitution for individual variables in formulas of the introduced language is defined. This definition is borrowed from [6]. For such purpose some auxiliary notation and propositions are introduced.

#### MML Identifier: CQC_LANG

The terminology and notation used in this paper have been introduced in the following articles [9] [11] [10] [12] [3] [4] [8] [2] [7] [1] [5]

Contents (PDF format)

#### Bibliography

[1] Grzegorz Bancerek. Connectives and subformulae of the first order language. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[3] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski and Grzegorz Bancerek. Variables in formulae of the first order language. Journal of Formalized Mathematics, 1, 1989.
[6] Witold A. Pogorzelski and Tadeusz Prucnal. The substitution rule for predicate letters in the first-order predicate calculus. \em Reports on Mathematical Logic, (5):77--90, 1975.
[7] Piotr Rudnicki and Andrzej Trybulec. A first order language. Journal of Formalized Mathematics, 1, 1989.
[8] Andrzej Trybulec. Binary operations applied to functions. Journal of Formalized Mathematics, 1, 1989.
[9] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[10] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[11] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[12] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.