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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 res...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2017
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| _version_ | 1867613504768311296 |
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| access_status_str | Open Access |
| author | Ouwehand, Peter |
| author2 | Rose, Henry |
| author_browse | Ouwehand, Peter Rose, Henry |
| author_facet | Rose, Henry Ouwehand, Peter |
| author_sort | Ouwehand, Peter |
| collection | Thesis |
| description | 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. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/25548 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:37:12.471Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2017 |
| publishDateRange | 2017 |
| publishDateSort | 2017 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/25548 The power function Ouwehand, Peter Rose, Henry Mathematics 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. 2017-10-11T08:04:53Z 2017-10-11T08:04:53Z 1993 2017-02-28T10:07:38Z Thesis http://hdl.handle.net/11427/25548 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town University of Cape Town |
| spellingShingle | Mathematics Ouwehand, Peter The power function |
| title | The power function |
| title_full | The power function |
| title_fullStr | The power function |
| title_full_unstemmed | The power function |
| title_short | The power function |
| title_sort | power function |
| topic | Mathematics |
| url | http://hdl.handle.net/11427/25548 |
| work_keys_str_mv | AT ouwehandpeter thepowerfunction AT ouwehandpeter powerfunction |