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.III24.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]. Wellformed 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.
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 firstorder
predicate calculus.
\em Reports on Mathematical Logic, (5):7790, 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.
Received May 11, 1990
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