Journal of Formalized Mathematics
Volume 8, 1996
University of Bialystok
Copyright (c) 1996 Association of Mizar Users

Institution of Many Sorted Algebras. Part I: Signature Reduct of an Algebra


Grzegorz Bancerek
Warsaw University, Bialystok

Summary.

In the paper the notation necessary to construct the institution of many sorted algebras is introduced.

MML Identifier: INSTALG1

The terminology and notation used in this paper have been introduced in the following articles [21] [14] [24] [25] [11] [8] [15] [1] [16] [2] [3] [9] [6] [22] [23] [13] [12] [10] [19] [18] [5] [20] [4] [17] [7]

Contents (PDF format)

  1. Preliminaries
  2. Subsignatures
  3. Signature reducts
  4. Translating homomorphisms

Bibliography

[1] Grzegorz Bancerek. K\"onig's theorem. Journal of Formalized Mathematics, 2, 1990.
[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. Terms over many sorted universal algebra. Journal of Formalized Mathematics, 6, 1994.
[5] Grzegorz Bancerek. Minimal signature for partial algebra. Journal of Formalized Mathematics, 7, 1995.
[6] Grzegorz Bancerek. Reduction relations. Journal of Formalized Mathematics, 7, 1995.
[7] Grzegorz Bancerek. Translations, endomorphisms, and stable equational theories. Journal of Formalized Mathematics, 8, 1996.
[8] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[9] Grzegorz Bancerek and Piotr Rudnicki. On defining functions on trees. Journal of Formalized Mathematics, 5, 1993.
[10] Ewa Burakowska. Subalgebras of many sorted algebra. Lattice of subalgebras. Journal of Formalized Mathematics, 6, 1994.
[11] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[12] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[13] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[14] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[15] Czeslaw Bylinski. Finite sequences and tuples of elements of a non-empty sets. Journal of Formalized Mathematics, 2, 1990.
[16] Patricia L. Carlson and Grzegorz Bancerek. Context-free grammar --- part I. Journal of Formalized Mathematics, 4, 1992.
[17] Artur Kornilowicz. On the group of automorphisms of universal algebra and many sorted algebra. Journal of Formalized Mathematics, 6, 1994.
[18] Malgorzata Korolkiewicz. Homomorphisms of many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[19] Beata Madras. Products of many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[20] Beata Perkowska. Free many sorted universal algebra. Journal of Formalized Mathematics, 6, 1994.
[21] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[22] Andrzej Trybulec. Many-sorted sets. Journal of Formalized Mathematics, 5, 1993.
[23] Andrzej Trybulec. Many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[24] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[25] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

Received December 30, 1996

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