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Logical presentations of domains
Bibliography: pages 168-174.
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2016
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| _version_ | 1867614317290979328 |
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| access_status_str | Open Access |
| author | Hulley, Hardy |
| author2 | Brink, Chris |
| author_browse | Brink, Chris Hulley, Hardy |
| author_facet | Brink, Chris Hulley, Hardy |
| author_sort | Hulley, Hardy |
| collection | Thesis |
| description | Bibliography: pages 168-174. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/17336 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:50:07.353Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| 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:11427/17336 Logical presentations of domains Hulley, Hardy Brink, Chris Mathematics Bibliography: pages 168-174. This thesis combines a fairly general overview of domain theory with a detailed examination of recent work which establishes a connection between domain theory and logic. To start with, the theory of domains is developed with such issues as the semantics of recursion and iteration; the solution of recursive domain equations; and non-determinism in mind. In this way, a reasonably comprehensive account of domains, as ordered sets, is given. The topological dimension of domain theory is then revealed, and the logical insights gained by regarding domains as topological spaces are emphasised. These logical insights are further reinforced by an examination of pointless topology and Stone duality. A few of the more prominent categories of domains are surveyed, and Stone-type dualities for the objects of some of these categories are presented. The above dualities are then applied to the task of presenting domains as logical theories. Two types of logical theory are considered, namely axiomatic systems, and Gentzen-style deductive systems. The way in which these theories describe domains is by capturing the relationships between the open subsets of domains. 2016-02-29T12:01:03Z 2016-02-29T12:01:03Z 1993 Master Thesis Masters MSc http://hdl.handle.net/11427/17336 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics Hulley, Hardy Logical presentations of domains |
| thesis_degree_str | Master's |
| title | Logical presentations of domains |
| title_full | Logical presentations of domains |
| title_fullStr | Logical presentations of domains |
| title_full_unstemmed | Logical presentations of domains |
| title_short | Logical presentations of domains |
| title_sort | logical presentations of domains |
| topic | Mathematics |
| url | http://hdl.handle.net/11427/17336 |
| work_keys_str_mv | AT hulleyhardy logicalpresentationsofdomains |