Journal of Formalized Mathematics
Volume 14, 2002
University of Bialystok
Copyright (c) 2002 Association of Mizar Users

Order Sorted Algebras


Josef Urban
Charles University, Praha

Summary.

Initial notions for order sorted algebras.

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

MML Identifier: OSALG_1

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

Contents (PDF format)

  1. Preliminaries
  2. The Notions: Order-Sorted, Discernable, Op-Discrete
  3. Order Sorted Signature

Acknowledgments

Thanks to Joseph Goguen, for providing me with his articles on osas, and Andrzej Trybulec, for suggesting and funding this work in Bialystok.

Bibliography

[1] Grzegorz Bancerek. K\"onig's theorem. Journal of Formalized Mathematics, 2, 1990.
[2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[3] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. Finite sequences and tuples of elements of a non-empty sets. Journal of Formalized Mathematics, 2, 1990.
[7] Adam Grabowski. On the category of posets. Journal of Formalized Mathematics, 8, 1996.
[8] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.
[9] Konrad Raczkowski and Pawel Sadowski. Equivalence relations and classes of abstraction. Journal of Formalized Mathematics, 1, 1989.
[10] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[11] Andrzej Trybulec. Many-sorted sets. Journal of Formalized Mathematics, 5, 1993.
[12] Andrzej Trybulec. Many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[13] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.
[14] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[15] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[16] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.
[17] Edmund Woronowicz and Anna Zalewska. Properties of binary relations. Journal of Formalized Mathematics, 1, 1989.

Received September 19, 2002

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