Computational Prospects of Infinity: Presented Talks, Part 2

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World Scientific, 2008 - Electronic books - 432 pages
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This volume is a collection of written versions of the talks given at the Workshop on Computational Prospects of Infinity, held at the Institute for Mathematical Sciences from 18 June to 15 August 2005. It consists of contributions from many of the leading experts in recursion theory (computability theory) and set theory. Topics covered include the structure theory of various notions of degrees of unsolvability, algorithmic randomness, reverse mathematics, forcing, large cardinals and inner model theory, and many others.
 

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Contents

Generating Sets for the Recursively Enumerable Turing Degrees Klaus AmbosSpies Ste en Lempp and Theodore A Slaman
1
Coding into Hw2 Together or Not with Forcing Axioms A Survey David Asper o
23
Nonstandard Methods in Ramseys Theorem for Pairs Chi Tat Chong
47
Prompt Simplicity Array Computability and Cupping Rod Downey Noam Greenberg Joseph S Miller and Rebecca Weber
59
Lowness for Computable Machines Rod Downey Noam Greenberg Nenad Mihailovi c and Andr e Nies
79
A Simpler Short Extenders Forcing Gap 3 Moti Gitik
87
Limit Computability and Constructive Measure Denis R Hirschfeldt and Sebastiaan A Terwijn
131
The Strength of Some Combinatorial Principles Related to Ramseys Theorem for Pairs Denis R Hirschfeldt Carl G Jockusch Jr Bj rn KjosHanssen Ste ...
143
Eliminating Concepts Andr e Nies
225
A Lower Cone in the wtt Degrees of NonIntegral Effective Dimension Andr e Nies and Jan Reimann
249
A Minimal rKDegree Alexander Raichev and Frank Stephan
261
Diamonds on P Masahiro Shioya
271
Rigidity and Biinterpretability in the Hyperdegrees Richard A Shore
299
Some Fundamental Issues Concerning Degrees of Unsolvability Stephen G Simpson
313
Weak Determinacy and Iterations of Inductive Definitions MedYahya Ould MedSalem and Kazuyuki Tanaka
333
A tt Version of the PosnerRobinson Theorem W Hugh Woodin
355

Absoluteness for Universally Baire Sets and the Uncountable II Ilijas Farah Richard Ketchersid Paul Larson and Menachem Magidor
163
Monadic Definability of Ordinals Itay Neeman
193
A Cuppable NonBounding Degree Keng Meng Ng
207
Cupping Computably Enumerable Degrees in the Ershov Hierarchy Guohua Wu
393
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