Journal of Formalized Mathematics
Volume 13, 2001
University of Bialystok
Copyright (c) 2001
Association of Mizar Users
Hierarchies and Classifications of Sets

Mariusz Giero

University of Bialystok
Summary.

This article is a continuation of [3] article. Further properties
of classification of sets are proved. The notion of hierarchy of a set
is introduced. Properties of partitions and hierarchies are shown. The main
theorem says that for each hierarchy there exists a classification
which union equals to the considered hierarchy.
This work has been partially supported by the European Community TYPES grant IST199929001
and CALCULEMUS grant HPRNCT200000102.
The terminology and notation used in this paper have been
introduced in the following articles
[9]
[2]
[12]
[6]
[13]
[1]
[14]
[10]
[7]
[8]
[5]
[11]
[4]
[3]

Tree and Classification of a Set

The Hierarchy of a Set

Some Properties of Partitions, Hierarchies and Classifications of Sets
Acknowledgments
I would like to thank Prof. Andrzej Trybulec for his help in the preparation
of this article.
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Received December 28, 2001
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