{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86790"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86790","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Decision Problems in the Lattice of P01 Classes","abstract":"Given an (undecidable) elementary theory of a computability-theoretic structure, it is natural to ask how much of the theory is decidable. An AE-sentence is a sentence in prenex normal form with all universal quantifiers preceding all existential quantifiers, and the AE-theory of a structure is the set of all AE-sentences true in the structure. In Chapter 3 we show that the AE-theory of ( LP01 , ∩, ∪, 0, 1) is decidable. In Chapter 4 we show that the AE-theories of ( LP01 , ∩, ∪, 0, 1) and ( LP01 * , ∩, ∪, 0, 1) are different and provide a decision procedure for the AE-theory of ( LP01 * , ∩, ∪, 0, 1).","abstract_html":"Given an (undecidable) elementary theory of a computability-theoretic structure, it is natural to ask how much of the theory is decidable. An AE-sentence is a sentence in prenex normal form with all universal quantifiers preceding all existential quantifiers, and the AE-theory of a structure is the set of all AE-sentences true in the structure. In Chapter 3 we show that the AE-theory of ( LP01 , ∩, ∪, 0, 1) is decidable. In Chapter 4 we show that the AE-theories of ( LP01 , ∩, ∪, 0, 1) and ( LP01 * , ∩, ∪, 0, 1) are different and provide a decision procedure for the AE-theory of ( LP01 * , ∩, ∪, 0, 1).","abstract_has_math":false,"creators":["Lawton, Linda Barker"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Jockusch, Carl G., Jr."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:19:33Z","date_published":"2015-09-28T15:19:33Z","updated_at":"2026-07-22T22:26:27Z","subjects":["Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3044154"],"render_values":[{"text":"(MiAaPQ)AAI3044154","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86790","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Jockusch, Carl G., Jr."]},{"key":"dc:creator","label":"Author","values":["Lawton, Linda Barker"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:19:33Z","10000-01-01","2002"]},{"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/2142/86790","(MiAaPQ)AAI3044154"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Given an (undecidable) elementary theory of a computability-theoretic structure, it is natural to ask how much of the theory is decidable. An AE-sentence is a sentence in prenex normal form with all universal quantifiers preceding all existential quantifiers, and the AE-theory of a structure is the set of all AE-sentences true in the structure. In Chapter 3 we show that the AE-theory of ( LP01 , ∩, ∪, 0, 1) is decidable. In Chapter 4 we show that the AE-theories of ( LP01 , ∩, ∪, 0, 1) and ( LP01 * , ∩, ∪, 0, 1) are different and provide a decision procedure for the AE-theory of ( LP01 * , ∩, ∪, 0, 1).","Made available in DSpace on 2015-09-28T15:19:33Z (GMT). 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An AE-sentence is a sentence in prenex normal form with all universal quantifiers preceding all existential quantifiers, and the AE-theory of a structure is the set of all AE-sentences true in the structure. In Chapter 3 we show that the AE-theory of ( LP01 , ∩, ∪, 0, 1) is decidable. In Chapter 4 we show that the AE-theories of ( LP01 , ∩, ∪, 0, 1) and ( LP01 * , ∩, ∪, 0, 1) are different and provide a decision procedure for the AE-theory of ( LP01 * , ∩, ∪, 0, 1).","Made available in DSpace on 2015-09-28T15:19:33Z (GMT). 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