Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/122318
Title: TURNING DEGREES CONSTRUCTIONS AND THEIR INDUCTION STRENGTH IN REVERSE MATHEMATICS
Authors: LIU YIQUN
Keywords: Mathematical logic,Computability theory,Reverse recursion theory,Turing degree,priority tree argument, induction strength
Issue Date: 14-Aug-2015
Source: LIU YIQUN (2015-08-14). TURNING DEGREES CONSTRUCTIONS AND THEIR INDUCTION STRENGTH IN REVERSE MATHEMATICS. ScholarBank@NUS Repository.
Abstract: In this thesis, we study Turing degrees in the context of classical computability theory (recursion Theory) and reverse recursion theory. In the first part, we prove that P + \Sigma_1 Induction proves the existence of isolated d.c.e. degrees and upper isolated d.c.e. degrees. We also prove that P + \Sigma_3 Induction verifies the existence of \Omega-c.e. universal cupping degrees. In the second part, we study another algebraic decomposition of R where R denotes the class of computably enumerable degrees. Ambos-Spies et al. (1984) proved that R = M \cup PS. We first define another subclass of R, STB, which consists of 0 together with all degrees for the base (set) in any Slaman triple. We will show R = STB \cup PS in the sense that given any c.e. set A, either there exist c.e. sets B and C such that (A,B,C) is a Slaman triple or A has promptly simple degree.
URI: http://scholarbank.nus.edu.sg/handle/10635/122318
Appears in Collections:Ph.D Theses (Open)

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