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

Subalgebras of an Order Sorted Algebra. Lattice of Subalgebras


Josef Urban
Charles University, Praha

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

MML Identifier: OSALG_2

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

Contents (PDF format)

  1. Auxiliary Facts about Order Sorted Sets
  2. Constants of an Order Sorted Algebra
  3. Subalgebras of an Order Sorted Algebra
  4. Order Sorted Subsets of an Order Sorted Algebra
  5. Operations on Subalgebras of an Order Sorted Algebra
  6. The Lattice of Subalgebras of an Order Sorted Algebra

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] Ewa Burakowska. Subalgebras of many sorted algebra. Lattice of subalgebras. Journal of Formalized Mathematics, 6, 1994.
[3] Czeslaw Bylinski. Binary operations. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[6] Artur Kornilowicz. Definitions and basic properties of boolean and union of many sorted sets. Journal of Formalized Mathematics, 7, 1995.
[7] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.
[8] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[9] Andrzej Trybulec. Many-sorted sets. Journal of Formalized Mathematics, 5, 1993.
[10] Andrzej Trybulec. Many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[11] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.
[12] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[13] Josef Urban. Order sorted algebras. Journal of Formalized Mathematics, 14, 2002.
[14] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[15] Stanislaw Zukowski. Introduction to lattice theory. Journal of Formalized Mathematics, 1, 1989.

Received September 19, 2002

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