The power function
| dc.contributor.advisor | Rose, Henry | |
| dc.contributor.author | Ouwehand, Peter | |
| dc.date.accessioned | 2017-10-11T08:04:53Z | |
| dc.date.available | 2017-10-11T08:04:53Z | |
| dc.date.issued | 1993 | |
| dc.date.updated | 2017-02-28T10:07:38Z | |
| dc.description.abstract | 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. | |
| dc.identifier.apacitation | Ouwehand, P. (1993). <i>The power function</i>. (). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/25548 | en_ZA |
| dc.identifier.chicagocitation | Ouwehand, Peter. <i>"The power function."</i> ., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1993. http://hdl.handle.net/11427/25548 | en_ZA |
| dc.identifier.citation | Ouwehand, P. 1993. The power function. University of Cape Town. | en_ZA |
| dc.identifier.ris | TY - Thesis / Dissertation AU - Ouwehand, Peter AB - 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. DA - 1993 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1993 T1 - The power function TI - The power function UR - http://hdl.handle.net/11427/25548 ER - | en_ZA |
| dc.identifier.uri | http://hdl.handle.net/11427/25548 | |
| dc.identifier.vancouvercitation | Ouwehand P. The power function. []. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1993 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/25548 | en_ZA |
| dc.language.iso | eng | |
| dc.publisher.department | Department of Mathematics and Applied Mathematics | |
| dc.publisher.faculty | Faculty of Science | |
| dc.publisher.institution | University of Cape Town | |
| dc.publisher.institution | University of Cape Town | |
| dc.subject.other | Mathematics | |
| dc.title | The power function | |
| dc.type | Thesis | |
| uct.type.filetype | ||
| uct.type.filetype | Text | |
| uct.type.filetype | Image |