{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/19193"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/19193","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Stable theories in functional analysis","abstract":"Model theory is the logical analysis of mathematical structures. The class of structures considered in model theory includes, among others, all structures from algebra, number theory, and finite-dimensional analysis. A limitation, however, is that this class does not include the families of structures that are studied functional analysis, e.g., Banach spaces, or operator algebras. This limitation lies in the fact that the discourse in analysis is carried out almost entirely in higher order logic, and the traditional logic of model theory is first order logic. Higher order logics do not have a powerful model theory.","abstract_html":"Model theory is the logical analysis of mathematical structures. The class of structures considered in model theory includes, among others, all structures from algebra, number theory, and finite-dimensional analysis. A limitation, however, is that this class does not include the families of structures that are studied functional analysis, e.g., Banach spaces, or operator algebras. This limitation lies in the fact that the discourse in analysis is carried out almost entirely in higher order logic, and the traditional logic of model theory is first order logic. Higher order logics do not have a powerful model theory.","abstract_has_math":false,"creators":["Iovino, Jose Nicolas"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["van den Dries, Lou"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T11:59:46Z","date_published":"2011-05-07T11:59:46Z","updated_at":"2026-07-22T22:25:12Z","subjects":["Mathematics"],"languages":["eng"],"rights":["Copyright 1994 Iovino, Jose Nicolas"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9512412","(UMI)AAI9512412"],"render_values":[{"text":"AAI9512412","href":null,"code":true},{"text":"(UMI)AAI9512412","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/19193","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["van den Dries, Lou"]},{"key":"dc:creator","label":"Author","values":["Iovino, Jose Nicolas"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T11:59:46Z","10000-01-01","1994"]},{"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"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1994 Iovino, Jose Nicolas"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9512412","(UMI)AAI9512412","http://hdl.handle.net/2142/19193"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Model theory is the logical analysis of mathematical structures. The class of structures considered in model theory includes, among others, all structures from algebra, number theory, and finite-dimensional analysis. A limitation, however, is that this class does not include the families of structures that are studied functional analysis, e.g., Banach spaces, or operator algebras. This limitation lies in the fact that the discourse in analysis is carried out almost entirely in higher order logic, and the traditional logic of model theory is first order logic. Higher order logics do not have a powerful model theory.","Recently, C. W. Henson has developed a model-theoretical apparatus that extends model theory to include important classes of structures from functional analysis preserving the desirable characteristics of first-order logic. One has, for instance, a compactness theorem and a Lowenheim-Skolem theorems for Banach spaces.","Some of the most remarkable results of Banach space theory in the last two decades have been proved by borrowing ideas from model theory (e.g., ultrapowers, stability). The apparatus described above provides a foundation for such contributions.","We have developed Henson's framework further, and introduced the fundamentals of classification theory (or stability theory) for structures based on Banach spaces.","Made available in DSpace on 2011-05-07T11:59:46Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9512412.pdf: 4977513 bytes, checksum: 225cea695b5349f2425a3e72a5d03061 (MD5) Previous issue date: 1994","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:35:17Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:13:51-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["Stable theories in functional analysis"]}]}],"canonical_facts":{"dc:contributor":["van den Dries, Lou"],"dc:creator":["Iovino, Jose Nicolas"],"dc:date":["2011-05-07T11:59:46Z","10000-01-01","1994"],"dc:description":["Model theory is the logical analysis of mathematical structures. The class of structures considered in model theory includes, among others, all structures from algebra, number theory, and finite-dimensional analysis. A limitation, however, is that this class does not include the families of structures that are studied functional analysis, e.g., Banach spaces, or operator algebras. This limitation lies in the fact that the discourse in analysis is carried out almost entirely in higher order logic, and the traditional logic of model theory is first order logic. Higher order logics do not have a powerful model theory.","Recently, C. W. Henson has developed a model-theoretical apparatus that extends model theory to include important classes of structures from functional analysis preserving the desirable characteristics of first-order logic. One has, for instance, a compactness theorem and a Lowenheim-Skolem theorems for Banach spaces.","Some of the most remarkable results of Banach space theory in the last two decades have been proved by borrowing ideas from model theory (e.g., ultrapowers, stability). The apparatus described above provides a foundation for such contributions.","We have developed Henson's framework further, and introduced the fundamentals of classification theory (or stability theory) for structures based on Banach spaces.","Made available in DSpace on 2011-05-07T11:59:46Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9512412.pdf: 4977513 bytes, checksum: 225cea695b5349f2425a3e72a5d03061 (MD5) Previous issue date: 1994","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:35:17Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:13:51-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["AAI9512412","(UMI)AAI9512412","http://hdl.handle.net/2142/19193"],"dc:language":["eng"],"dc:rights":["Copyright 1994 Iovino, Jose Nicolas"],"dc:subject":["Mathematics"],"dc:title":["Stable theories in functional analysis"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:12Z"}