Journal of Formalized Mathematics
Volume 5, 1993
University of Bialystok
Copyright (c) 1993 Association of Mizar Users

Free Universal Algebra Construction


Beata Perkowska
Warsaw University, Bialystok

Summary.

A construction of the free universal algebra with fixed signature and a given set of generators.

MML Identifier: FREEALG

The terminology and notation used in this paper have been introduced in the following articles [15] [18] [16] [19] [7] [9] [4] [8] [14] [10] [1] [2] [3] [17] [13] [6] [11] [5] [12]

Contents (PDF format)

  1. Preliminaries
  2. Free Universal Algebra --- General Notions
  3. Construction of Decorated Tree Structure for Free Universal Algebra
  4. Construction of Free Universal Algebra for Non-empty Set of Generators and Given Signature
  5. Construction of Free Universal Algebra and Set of Generators

Bibliography

[1] Grzegorz Bancerek. K\"onig's Lemma. Journal of Formalized Mathematics, 3, 1991.
[2] Grzegorz Bancerek. Sets and functions of trees and joining operations of trees. Journal of Formalized Mathematics, 4, 1992.
[3] Grzegorz Bancerek. Joining of decorated trees. Journal of Formalized Mathematics, 5, 1993.
[4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[5] Grzegorz Bancerek and Piotr Rudnicki. On defining functions on trees. Journal of Formalized Mathematics, 5, 1993.
[6] Ewa Burakowska. Subalgebras of the universal algebra. Lattices of subalgebras. Journal of Formalized Mathematics, 5, 1993.
[7] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[8] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[9] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[10] Czeslaw Bylinski. Finite sequences and tuples of elements of a non-empty sets. Journal of Formalized Mathematics, 2, 1990.
[11] Patricia L. Carlson and Grzegorz Bancerek. Context-free grammar --- part I. Journal of Formalized Mathematics, 4, 1992.
[12] Malgorzata Korolkiewicz. Homomorphisms of algebras. Quotient universal algebra. Journal of Formalized Mathematics, 5, 1993.
[13] Jaroslaw Kotowicz, Beata Madras, and Malgorzata Korolkiewicz. Basic notation of universal algebra. Journal of Formalized Mathematics, 4, 1992.
[14] Andrzej Trybulec. Binary operations applied to functions. Journal of Formalized Mathematics, 1, 1989.
[15] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[16] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[17] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
[18] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[19] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.

Received October 20, 1993


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