{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86786"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86786","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Contributions to the Model Theory of Fields and Compact Complex Spaces","abstract":"\"While the methods of geometric stability theory have traditionally been applied to algebraic rather than analytic geometry, it has been observed that these techniques are also meaningful when applied to compact complex analytic spaces. One obstacle is that these structures are not saturated in the natural language of their analytic sets. The notion of a Zariski closed set in an elementary extension of a compact complex space, as well as the associated complex dimension, are discussed. It is shown that a one-dimensional Zariski closed set in an elementary extension of a compact complex space is essentially algebraic. This provides a kind of nonstandard version of the Riemann Existence Theorem. The notion of a \"\"saturated\"\" compact complex analytic space, where it is not necessary to pass to elementary extensions, is also introduced. A characterisation of such spaces in terms of the Douady spaces of their cartesian powers, as well as an application to relative algebraic reductions, is given.\"","abstract_html":""While the methods of geometric stability theory have traditionally been applied to algebraic rather than analytic geometry, it has been observed that these techniques are also meaningful when applied to compact complex analytic spaces. One obstacle is that these structures are not saturated in the natural language of their analytic sets. The notion of a Zariski closed set in an elementary extension of a compact complex space, as well as the associated complex dimension, are discussed. It is shown that a one-dimensional Zariski closed set in an elementary extension of a compact complex space is essentially algebraic. This provides a kind of nonstandard version of the Riemann Existence Theorem. The notion of a ""saturated"" compact complex analytic space, where it is not necessary to pass to elementary extensions, is also introduced. A characterisation of such spaces in terms of the Douady spaces of their cartesian powers, as well as an application to relative algebraic reductions, is given."","abstract_has_math":false,"creators":["Moosa, Rahim Nazim"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Pillay, Anand"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:19:32Z","date_published":"2015-09-28T15:19:32Z","updated_at":"2026-07-22T22:26:27Z","subjects":["Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3023146"],"render_values":[{"text":"(MiAaPQ)AAI3023146","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86786","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Pillay, Anand"]},{"key":"dc:creator","label":"Author","values":["Moosa, Rahim Nazim"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:19:32Z","10000-01-01","2001"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/86786","(MiAaPQ)AAI3023146"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"While the methods of geometric stability theory have traditionally been applied to algebraic rather than analytic geometry, it has been observed that these techniques are also meaningful when applied to compact complex analytic spaces. One obstacle is that these structures are not saturated in the natural language of their analytic sets. The notion of a Zariski closed set in an elementary extension of a compact complex space, as well as the associated complex dimension, are discussed. It is shown that a one-dimensional Zariski closed set in an elementary extension of a compact complex space is essentially algebraic. This provides a kind of nonstandard version of the Riemann Existence Theorem. The notion of a \"\"saturated\"\" compact complex analytic space, where it is not necessary to pass to elementary extensions, is also introduced. A characterisation of such spaces in terms of the Douady spaces of their cartesian powers, as well as an application to relative algebraic reductions, is given.\"","Made available in DSpace on 2015-09-28T15:19:32Z (GMT). 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One obstacle is that these structures are not saturated in the natural language of their analytic sets. The notion of a Zariski closed set in an elementary extension of a compact complex space, as well as the associated complex dimension, are discussed. It is shown that a one-dimensional Zariski closed set in an elementary extension of a compact complex space is essentially algebraic. This provides a kind of nonstandard version of the Riemann Existence Theorem. The notion of a \"\"saturated\"\" compact complex analytic space, where it is not necessary to pass to elementary extensions, is also introduced. A characterisation of such spaces in terms of the Douady spaces of their cartesian powers, as well as an application to relative algebraic reductions, is given.\"","Made available in DSpace on 2015-09-28T15:19:32Z (GMT). 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