Volume 14, 2002

University of Bialystok

Copyright (c) 2002 Association of Mizar Users

**Josef Urban**- Charles University, Praha

- Free Order Sorted Universal Algebra - the general construction for any locally directed signatures.

This work was done during author's research visit in Bialystok, funded by the CALCULEMUS grant HPRN-CT-2000-00102.

- Preliminaries
- Construction of Free Order Sorted Algebras for Given Signature
- Minimal Terms

- [1]
Grzegorz Bancerek.
Curried and uncurried functions.
*Journal of Formalized Mathematics*, 2, 1990. - [2]
Grzegorz Bancerek.
K\"onig's theorem.
*Journal of Formalized Mathematics*, 2, 1990. - [3]
Grzegorz Bancerek.
Cartesian product of functions.
*Journal of Formalized Mathematics*, 3, 1991. - [4]
Grzegorz Bancerek.
K\"onig's Lemma.
*Journal of Formalized Mathematics*, 3, 1991. - [5]
Grzegorz Bancerek.
Sets and functions of trees and joining operations of trees.
*Journal of Formalized Mathematics*, 4, 1992. - [6]
Grzegorz Bancerek.
Joining of decorated trees.
*Journal of Formalized Mathematics*, 5, 1993. - [7]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
*Journal of Formalized Mathematics*, 1, 1989. - [8]
Grzegorz Bancerek and Piotr Rudnicki.
On defining functions on trees.
*Journal of Formalized Mathematics*, 5, 1993. - [9]
Ewa Burakowska.
Subalgebras of many sorted algebra. Lattice of subalgebras.
*Journal of Formalized Mathematics*, 6, 1994. - [10]
Czeslaw Bylinski.
Functions and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [11]
Czeslaw Bylinski.
Functions from a set to a set.
*Journal of Formalized Mathematics*, 1, 1989. - [12]
Czeslaw Bylinski.
Partial functions.
*Journal of Formalized Mathematics*, 1, 1989. - [13]
Czeslaw Bylinski.
Some basic properties of sets.
*Journal of Formalized Mathematics*, 1, 1989. - [14]
Czeslaw Bylinski.
Finite sequences and tuples of elements of a non-empty sets.
*Journal of Formalized Mathematics*, 2, 1990. - [15]
Patricia L. Carlson and Grzegorz Bancerek.
Context-free grammar --- part I.
*Journal of Formalized Mathematics*, 4, 1992. - [16]
Malgorzata Korolkiewicz.
Homomorphisms of many sorted algebras.
*Journal of Formalized Mathematics*, 6, 1994. - [17]
Malgorzata Korolkiewicz.
Many sorted quotient algebra.
*Journal of Formalized Mathematics*, 6, 1994. - [18]
Beata Madras.
Product of family of universal algebras.
*Journal of Formalized Mathematics*, 5, 1993. - [19]
Andrzej Nedzusiak.
$\sigma$-fields and probability.
*Journal of Formalized Mathematics*, 1, 1989. - [20]
Beata Perkowska.
Free many sorted universal algebra.
*Journal of Formalized Mathematics*, 6, 1994. - [21]
Konrad Raczkowski and Pawel Sadowski.
Equivalence relations and classes of abstraction.
*Journal of Formalized Mathematics*, 1, 1989. - [22]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [23]
Andrzej Trybulec.
Tuples, projections and Cartesian products.
*Journal of Formalized Mathematics*, 1, 1989. - [24]
Andrzej Trybulec.
Many-sorted sets.
*Journal of Formalized Mathematics*, 5, 1993. - [25]
Andrzej Trybulec.
Many sorted algebras.
*Journal of Formalized Mathematics*, 6, 1994. - [26]
Wojciech A. Trybulec.
Partially ordered sets.
*Journal of Formalized Mathematics*, 1, 1989. - [27]
Wojciech A. Trybulec.
Pigeon hole principle.
*Journal of Formalized Mathematics*, 2, 1990. - [28]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [29]
Josef Urban.
Homomorphisms of order sorted algebras.
*Journal of Formalized Mathematics*, 14, 2002. - [30]
Josef Urban.
Order sorted algebras.
*Journal of Formalized Mathematics*, 14, 2002. - [31]
Josef Urban.
Order sorted quotient algebra.
*Journal of Formalized Mathematics*, 14, 2002. - [32]
Josef Urban.
Subalgebras of a order sorted algebra. Lattice of subalgebras.
*Journal of Formalized Mathematics*, 14, 2002. - [33]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [34]
Edmund Woronowicz.
Relations defined on sets.
*Journal of Formalized Mathematics*, 1, 1989. - [35]
Edmund Woronowicz and Anna Zalewska.
Properties of binary relations.
*Journal of Formalized Mathematics*, 1, 1989.

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