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Jockusch, Carl G., Jr. Blaylock, Richard Warren 2011-05-07T13:41:37Z 2011-05-07T13:41:37Z 10000-01-01 1991 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 AAI9210749 (UMI)AAI9210749 http://hdl.handle.net/2142/22493 eng Copyright 1991 Blaylock, Richard Warren Mathematics Some results on e-genericity and recursively enumerable weak truth table degrees text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.