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

Boolean Posets, Posets under Inclusion and Products of Relational Structures


Adam Grabowski
Warsaw University, Bialystok
Robert Milewski
Warsaw University, Bialystok

Summary.

In the paper some notions useful in formalization of [11] are introduced, e.g. the definition of the poset of subsets of a set with inclusion as an ordering relation. Using the theory of many sorted sets authors formulate the definition of product of relational structures.

This work was partially supported by Office of Naval Research Grant N00014-95-1-1336.

MML Identifier: YELLOW_1

The terminology and notation used in this paper have been introduced in the following articles [17] [9] [20] [21] [23] [22] [15] [5] [6] [10] [1] [8] [7] [19] [24] [12] [3] [16] [14] [18] [2] [13] [4]

Contents (PDF format)

  1. Boolean Posets and Posets under Inclusion
  2. Products of Relational Structures

Acknowledgments

The authors would like to express their gratitude to Professor Andrzej Trybulec for his help in formulating mizared definition of the product.

Bibliography

[1] Grzegorz Bancerek. Zermelo theorem and axiom of choice. 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. Bounds in posets and relational substructures. Journal of Formalized Mathematics, 8, 1996.
[5] Jozef Bialas. Group and field definitions. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[7] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[8] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[9] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[10] Agata Darmochwal. Families of subsets, subspaces and mappings in topological spaces. Journal of Formalized Mathematics, 1, 1989.
[11] G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M. Mislove, and D.S. Scott. \em A Compendium of Continuous Lattices. Springer-Verlag, Berlin, Heidelberg, New York, 1980.
[12] Adam Grabowski. On the category of posets. Journal of Formalized Mathematics, 8, 1996.
[13] Beata Madras. Product of family of universal algebras. Journal of Formalized Mathematics, 5, 1993.
[14] Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec, and Pauline N. Kawamoto. Preliminaries to circuits, I. Journal of Formalized Mathematics, 6, 1994.
[15] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.
[16] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[17] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[18] Andrzej Trybulec. Many-sorted sets. Journal of Formalized Mathematics, 5, 1993.
[19] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.
[20] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[21] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[22] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.
[23] Edmund Woronowicz and Anna Zalewska. Properties of binary relations. Journal of Formalized Mathematics, 1, 1989.
[24] Stanislaw Zukowski. Introduction to lattice theory. Journal of Formalized Mathematics, 1, 1989.

Received September 20, 1996

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