Journal of Formalized Mathematics
Volume 12, 2000
University of Bialystok
Copyright (c) 2000
Association of Mizar Users
Basic Facts about Inaccessible and Measurable Cardinals

Josef Urban

Charles University, Praha
Summary.

Inaccessible, strongly inaccessible and measurable cardinals
are defined,
and it is proved that a measurable cardinal is strongly inaccessible. Filters
on sets are defined, some facts related to the section about cardinals
are proved. Existence of the Ulam matrix on nonlimit cardinals is proved.
The terminology and notation used in this paper have been
introduced in the following articles
[13]
[10]
[14]
[15]
[8]
[7]
[12]
[11]
[2]
[9]
[3]
[1]
[4]
[5]
[6]

Some Facts about Filters and Ideals on Sets

Inaccessible and Measurable Cardinals, {U}lam Matrix
Bibliography
 [1]
Grzegorz Bancerek.
Cardinal numbers.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Grzegorz Bancerek.
The ordinal numbers.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Grzegorz Bancerek.
Sequences of ordinal numbers.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Grzegorz Bancerek.
Cardinal arithmetics.
Journal of Formalized Mathematics,
2, 1990.
 [5]
Grzegorz Bancerek.
K\"onig's theorem.
Journal of Formalized Mathematics,
2, 1990.
 [6]
Grzegorz Bancerek.
On powers of cardinals.
Journal of Formalized Mathematics,
4, 1992.
 [7]
Czeslaw Bylinski.
Binary operations.
Journal of Formalized Mathematics,
1, 1989.
 [8]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [10]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [11]
Agata Darmochwal.
Finite sets.
Journal of Formalized Mathematics,
1, 1989.
 [12]
Beata Padlewska.
Families of sets.
Journal of Formalized Mathematics,
1, 1989.
 [13]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [14]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [15]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received April 14, 2000
[
Download a postscript version,
MML identifier index,
Mizar home page]