Global Properties of the Turing Degrees and the Turing Jump

Global Properties of the Turing Degrees and the Turing Jump

Cached

Download Links

[math.berkeley.edu]

by Theodore A. Slaman

Citations:

1 - 0 self

BibTeX

@MISC{Slaman_globalproperties,
    author = {Theodore A. Slaman},
    title = {Global Properties of the Turing Degrees and the Turing Jump},
    year = {}
}

Bookmark

OpenURL

Abstract

We present a summary of the lectures delivered to the Institute for Mathematical Sciences, Singapore, during the 2005 Summer School in Mathematical Logic. The lectures covered topics on the global structure of the Turing degrees D, the countability of its automorphism group, and the definability of the Turing jump within D.

Citations

66	Degrees of Unsolvability - Lerman - 1983
31	The upper semi-lattice of degrees of recursive unsolvability - Kleene, Post - 1954
27	Pseudo-jump operators II: transfinite iterations, hierarchies and minimal covers - Shore - 1984
24	A criterion for completeness of degrees of unsolvability - Friedberg - 1957
23	Degrees joining to 0 - Posner, Robinson - 1981
21	1968], Distributive initial segments of the degrees of unsolvability - Lachlan
15	First order theory of the degrees of recursive unsolvability - Simpson
12	Initial segments of the degrees of unsolvability - Lerman - 1971
12	Reducibility orderings: theories, definability and automorphisms - Nerode, Shore - 1980
10	Defining the Turing jump - Shore, Slaman - 1999
9	On the ∀∃-sentences of α-recursion theory - Shore - 1978
8	Automorphism bases for degrees of unsolvability - Jockusch, Posner - 1981
4	On suborderings of degrees of recursive unsolvability - Sacks - 1961
4	The problem of predicativity - Shoenfield - 1961
3	Countable initial segments of the degrees - Lachlan, Lebeuf - 1976
3	Global properties of local structures of degrees - Odifreddi, Shore - 1991
2	Upper cones as automorphism bases - Cooper - 1999
1	Direct and local definitions of the Turing jump. preprint - Shore - 2007