Journal of Formalized Mathematics
Volume 8, 1996
University of Bialystok
Copyright (c) 1996 Association of Mizar Users

More on the Lattice of Congruences in Many Sorted Algebra


Robert Milewski
Warsaw University, Bialystok

MML Identifier: MSUALG_8

The terminology and notation used in this paper have been introduced in the following articles [16] [8] [19] [14] [20] [21] [1] [5] [7] [6] [9] [4] [2] [15] [22] [3] [17] [11] [18] [10] [12] [13]

Contents (PDF format)

  1. More on the Lattice of Equivalence Relations
  2. Lattice of Congruences in Many Sorted Algebra as Sublattice of Lattice of Many Sorted Equivalence Relations Inherited Sup's and Inf's

Bibliography

[1] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek. K\"onig's theorem. Journal of Formalized Mathematics, 2, 1990.
[3] Grzegorz Bancerek. Complete lattices. Journal of Formalized Mathematics, 4, 1992.
[4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[7] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[8] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[9] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[10] Malgorzata Korolkiewicz. Many sorted quotient algebra. Journal of Formalized Mathematics, 6, 1994.
[11] Beata Madras. Products of many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[12] Robert Milewski. Lattice of congruences in many sorted algebra. Journal of Formalized Mathematics, 8, 1996.
[13] Robert Milewski. More on the lattice of many sorted equivalence relations. Journal of Formalized Mathematics, 8, 1996.
[14] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.
[15] Konrad Raczkowski and Pawel Sadowski. Equivalence relations and classes of abstraction. Journal of Formalized Mathematics, 1, 1989.
[16] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[17] Andrzej Trybulec. Many-sorted sets. Journal of Formalized Mathematics, 5, 1993.
[18] Andrzej Trybulec. Many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[19] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[20] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[21] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.
[22] Stanislaw Zukowski. Introduction to lattice theory. Journal of Formalized Mathematics, 1, 1989.

Received March 6, 1996


[ Download a postscript version, MML identifier index, Mizar home page]