Volume 8, 1996

University of Bialystok

Copyright (c) 1996 Association of Mizar Users

**Grzegorz Bancerek**- Warsaw University, Bialystok

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

- Preliminaries
- Subsignatures
- Signature reducts
- Translating homomorphisms

- [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.

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