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

Agata Darmochwal

Warsaw University, Bialystok

Supported by RPBP.III24.C1.
Summary.

A continuation of [7], with an axiom system
of firstorder predicate theory.
The consequence Cn of a set of formulas $X$ is defined as the
intersection of all theories containing $X$ and some basic properties of it
has been proved (monotonicity, idempotency, completeness
etc.). The notion of a proof of given formula is also introduced and it
is shown that ${\rm Cn} X = \{~p: p $ has a proof w.r.t. $ X\}$.
First 14 theorems are rather simple facts. I just wanted them to be included
in the data base.
The terminology and notation used in this paper have been
introduced in the following articles
[10]
[6]
[12]
[2]
[13]
[5]
[3]
[1]
[8]
[4]
[11]
[9]
[7]
Contents (PDF format)
Bibliography
 [1]
Grzegorz Bancerek.
The fundamental properties of natural numbers.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Grzegorz Bancerek.
The ordinal numbers.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Grzegorz Bancerek.
Sequences of ordinal numbers.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Czeslaw Bylinski.
A classical first order language.
Journal of Formalized Mathematics,
2, 1990.
 [8]
Agata Darmochwal.
Finite sets.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Piotr Rudnicki and Andrzej Trybulec.
A first order language.
Journal of Formalized Mathematics,
1, 1989.
 [10]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [11]
Andrzej Trybulec.
Tuples, projections and Cartesian products.
Journal of Formalized Mathematics,
1, 1989.
 [12]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [13]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received May 25, 1990
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