The power function

The axioms of ZFC provide very little information about the possible values of the power function (i.e. the map K---->2ᴷ). In this dissertation, we examine various theorems concerning the behaviour of the power function inside the formal system ZFC , and we :;hall be p:trticul:trly interested in results which provide eonstraints on the possible values of the power function. Thus most of the results presented here will be consistency results. A theorem of Easton (Theorem 2.3.1) shows that, when restricted to regular cardinals, the power function may take on any reasonable value, and thus a considerable part of this thesis is concerned with the power function on singular cardinals. We also examine the influence of various strong axioms of infinity, and their generalization to smaller cardinals, on the possible behaviour of the power function.

Grantor dc:publisher.institution

Department of Mathematics and Applied Mathematics

Year dc:date.issued

1993

Author dc:creator

• Ouwehand, Peter

Advisor dc:contributor.advisor

• Rose, Henry

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/22201

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/22201