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
HPRNCT200000102.
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]

Auxiliary Facts about Order Sorted Sets

Constants of an Order Sorted Algebra

Subalgebras of an Order Sorted Algebra

Order Sorted Subsets of an Order Sorted Algebra

Operations on Subalgebras of an Order Sorted Algebra

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.
Manysorted 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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