Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Selectivity and Weakly Compact Cardinals

Selectivity and Weakly Compact Cardinals E. C. MILNER 1. Introduction Lower case greek letters always denote ordinal numbers and, as usual, an ordinal a = {p: p < a} is the set of all smaller ordinals. The cofinality cf (a) of a is the least ordinal p for which there is a map / : p -> a whose range is cofinal in a, that is, for any y < a there is S < p such that /(<5) ^ y. If S is a set of ordinals we write sup(S) = US to denote the least ordinal a such that a ^ ft for all peS. Cardinal numbers are initial ordinal numbers and we denote these by K or by the letters K,X,II. The cardinal successor of K is K , the least cardinal greater than K. A cardinal K is regular if cf(/c) = K and singular if cf(/c) < K. For any set A, we denote the cardinal of A by \A\. Also if A is any cardinal we write [/1] = {X ^ A : \X\ = X} and < k [A] = {X ^ A:\X\ < X]. The cardinal K is strongly inaccessible if it is regular and 2^ http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

Selectivity and Weakly Compact Cardinals

Download PDF
5 pages

Loading next page...
 
/lp/wiley/selectivity-and-weakly-compact-cardinals-PBAAkzn89e

References (0)

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/14.4.329
Publisher site
See Article on Publisher Site

Abstract

E. C. MILNER 1. Introduction Lower case greek letters always denote ordinal numbers and, as usual, an ordinal a = {p: p < a} is the set of all smaller ordinals. The cofinality cf (a) of a is the least ordinal p for which there is a map / : p -> a whose range is cofinal in a, that is, for any y < a there is S < p such that /(<5) ^ y. If S is a set of ordinals we write sup(S) = US to denote the least ordinal a such that a ^ ft for all peS. Cardinal numbers are initial ordinal numbers and we denote these by K or by the letters K,X,II. The cardinal successor of K is K , the least cardinal greater than K. A cardinal K is regular if cf(/c) = K and singular if cf(/c) < K. For any set A, we denote the cardinal of A by \A\. Also if A is any cardinal we write [/1] = {X ^ A : \X\ = X} and < k [A] = {X ^ A:\X\ < X]. The cardinal K is strongly inaccessible if it is regular and 2^

Journal

Bulletin of the London Mathematical Society – Wiley

Published: Jul 1, 1982

There are no references for this article.