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This volume presents the lecture notes of short courses given by three leading experts in mathematical logic at the 2012 Asian Initiative for Infinity Logic Summer School . The major topics cover set-theoretic forcing, higher recursion theory, and applications of set theory to C*-algebra. This volume offers a wide spectrum of ideas and techniques introduced in contemporary research in the field of mathematical logic to students, researchers and mathematicians. Contents: Selected Applications of Logic to Classification Problem for C*-Algebras (Ilijas Farah); Subcomplete Forcing and L-Forcing (R

Recursion theory. --- Forcing (Model theory) --- C*-algebras. --- Algebras, C star --- Algebras, W star --- C star algebras --- W star algebras --- W*-algebras --- Banach algebras --- Model theory --- Logic, Symbolic and mathematical

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This monograph presents recursion theory from a generalized point of view centered on the computational aspects of definability. A major theme is the study of the structures of degrees arising from two key notions of reducibility, the Turing degrees and the hyperdegrees, using techniques and ideas from recursion theory, hyperarithmetic theory, and descriptive set theory. The emphasis is on the interplay between recursion theory and set theory, anchored on the notion of definability. The monograph covers a number of fundamental results in hyperarithmetic theory as well as some recent results on the structure theory of Turing and hyperdegrees. It also features a chapter on the applications of these investigations to higher randomness.

Recursion theory. --- Logic, Symbolic and mathematical --- Higher Randomness. --- Hyperdegrees. --- Jump Operator. --- Recursion Theory. --- Turing Degrees.

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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.

Set theory --- Recursion theory --- Infinite --- Infinity --- Finite, The --- Logic, Symbolic and mathematical

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Southeast Asian Conference on Logic

Logic, Symbolic and mathematical --- Logique symbolique et mathématique --- Congresses. --- Congrès --- Logic, symbolic and mathematical --- Congresses --- -Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- -Congresses --- Logic, Symbolic and mathematical - Congresses