{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/22493"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/22493","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Some results on e-genericity and recursively enumerable weak truth table degrees","abstract":"In this manuscript we explore two topics in recursion theory and their interaction.","abstract_html":"In this manuscript we explore two topics in recursion theory and their interaction.","abstract_has_math":false,"creators":["Blaylock, Richard Warren"],"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":2011,"date_issued":"2011-05-07T13:41:37Z","date_published":"2011-05-07T13:41:37Z","updated_at":"2026-07-22T22:25:20Z","subjects":["Mathematics"],"languages":["eng"],"rights":["Copyright 1991 Blaylock, Richard Warren"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9210749","(UMI)AAI9210749"],"render_values":[{"text":"AAI9210749","href":null,"code":true},{"text":"(UMI)AAI9210749","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/22493","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":["Blaylock, Richard Warren"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T13:41:37Z","10000-01-01","1991"]},{"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 1991 Blaylock, Richard Warren"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9210749","(UMI)AAI9210749","http://hdl.handle.net/2142/22493"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this manuscript we explore two topics in recursion theory and their interaction.","The first topic is e-genericity, a notion of genericity for recursively enumerable (r.e.) sets introduced by C. G. Jockusch, Jr. The second is weak truth table reducibility (w-reducibility), a strong reducibility (i.e., stronger than the most general Turing reducibility) first introduced by Friedberg and Rogers. In Chapter 1 we give a brief introduction to these topics and establish the relevant terminology and notation.","In Chapter 2 we give some closure and non-closure properties for the classes of e-generic sets and degrees, which are predicted by analogous results for previous notions of genericity. For example, the e-generic sets are not closed under union, intersection, or join, but on the other hand if the join $A \\oplus B$ of two sets is e-generic, then so are $A,B, A \\cup B$, and $A \\cap B$.","In Chapter 3 we investigate the structure of the weak truth table degrees (w-degrees) inside an e-generic Turing degree. Here we show that e-generic Turing degrees are highly noncontiguous in the sense that they contain no greatest and no least r.e. w-degree.","Finally in Chapter 4 we obtain some results on the ordering of the r.e. w-degrees in general. The main result is the existence of a nontrivial r.e. w-degree a which has a greatest lower bound with every r.e. w-degree b. We also show that these nontrivial completely cappable degrees can neither be low nor promptly simple.","Made available in DSpace on 2011-05-07T13:41:37Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9210749.pdf: 2722683 bytes, checksum: 07c8b9b10ac798d598fefb5475260d9f (MD5) Previous issue date: 1991","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:57:59Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:27:14-05:00 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":["Some results on e-genericity and recursively enumerable weak truth table degrees"]}]}],"canonical_facts":{"dc:contributor":["Jockusch, Carl G., Jr."],"dc:creator":["Blaylock, Richard Warren"],"dc:date":["2011-05-07T13:41:37Z","10000-01-01","1991"],"dc:description":["In this manuscript we explore two topics in recursion theory and their interaction.","The first topic is e-genericity, a notion of genericity for recursively enumerable (r.e.) sets introduced by C. G. Jockusch, Jr. The second is weak truth table reducibility (w-reducibility), a strong reducibility (i.e., stronger than the most general Turing reducibility) first introduced by Friedberg and Rogers. In Chapter 1 we give a brief introduction to these topics and establish the relevant terminology and notation.","In Chapter 2 we give some closure and non-closure properties for the classes of e-generic sets and degrees, which are predicted by analogous results for previous notions of genericity. For example, the e-generic sets are not closed under union, intersection, or join, but on the other hand if the join $A \\oplus B$ of two sets is e-generic, then so are $A,B, A \\cup B$, and $A \\cap B$.","In Chapter 3 we investigate the structure of the weak truth table degrees (w-degrees) inside an e-generic Turing degree. Here we show that e-generic Turing degrees are highly noncontiguous in the sense that they contain no greatest and no least r.e. w-degree.","Finally in Chapter 4 we obtain some results on the ordering of the r.e. w-degrees in general. The main result is the existence of a nontrivial r.e. w-degree a which has a greatest lower bound with every r.e. w-degree b. We also show that these nontrivial completely cappable degrees can neither be low nor promptly simple.","Made available in DSpace on 2011-05-07T13:41:37Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9210749.pdf: 2722683 bytes, checksum: 07c8b9b10ac798d598fefb5475260d9f (MD5) Previous issue date: 1991","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:57:59Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:27:14-05:00 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":["AAI9210749","(UMI)AAI9210749","http://hdl.handle.net/2142/22493"],"dc:language":["eng"],"dc:rights":["Copyright 1991 Blaylock, Richard Warren"],"dc:subject":["Mathematics"],"dc:title":["Some results on e-genericity and recursively enumerable weak truth table degrees"],"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":"2026-07-22T22:25:20Z"}