Computational prospects of infinity Part II, Presented talks / editors, Chitat Chong ... [et al.].

Format:

Book

Conference/Event

Contributor:

Chong, C.-T. (Chi-Tat), 1949-

Conference Name:

Workshop on Computational Prospects of Infinity (2005 : Institute for Mathematical Sciences, National University of Singapore)

Series:

Lecture notes series (National University of Singapore. Institute for Mathematical Sciences) ; 15.

Lecture notes series / Institute for Mathematical Sciences, National University of Singapore, 1793-0758 ; 15

Language:

English

Subjects (All):

Set theory--Congresses.

Set theory.

Recursion theory--Congresses.

Recursion theory.

Infinite--Congresses.

Infinite.

Physical Description:

1 online resource (432 p.)

Place of Publication:

Hackensack, NJ : World Scientific, c2008.

Language Note:

English

Summary:

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.

Contents:

CONTENTS; Foreword; Preface; Generating Sets for the Recursively Enumerable Turing Degrees Klaus Ambos-Spies, Ste en Lempp and Theodore A. Slaman; 1. Introduction; 2. The technical theorem and some intuition for its proof; 2.1. Requirements and simple strategies; 2.2. Strategies; 2.2.1. Making Θ = A: σ0(Θ); 2.2.2. Measuring whether the equations hold: σ1(X, Y,Λa,x,Λa,y,Λxy,a); 2.2.3. Computations between B, C, and X: σ2(X, Y,Λa,x,Λa,y,Λxy,a); 2.2.4. Making C the infimum of CD and CE: s3(X, Y,.a,x,.a,y,.xy,a,.cd,.ce)

2.2.5. Making Θa(A) = D and Θa(A) = E: σ4(X, Y,Λa,x,Λa,y,Λxy,a,Θa) and σ5(X, Y,Λa,x,Λa,y,Λxy,a,Θa)2.2.6. If Θby(BY ) = A then y,a(Y ) = A: σ6(X, Y,Λa,x,Λa,y,Λxy,a,Θby); 2.2.7. One sequence (X, Y,Λa,x,Λa,y,Λxy,a); 3. The global construction; 3.1. Interactions between σ-strategies; 3.2. The tree of strategies; 3.2.1. η-con.gurations; 3.3. The construction; 3.3.1. Adding an A-diagonalization strategy σ0; 3.3.2. Adding a σ1(X, Y,Λa,x,Λa,y,Λxy,a); 3.3.3. Adding a σ2(X, Y,Λa,x,Λa,y,Λxy,a); 3.3.4. Adding a σ3(X, Y,Λa,x,Λa,y,Λxy,a,Ψcd,Ψce)

3.3.5. Adding a σ4(X, Y,Λa,x,Λa,y,Λxy,a,Θa) or a σ5(X, Y,Λa,x,Λa,y,Λxy,a,Θa)3.3.6. Adding a σ6(X, Y,Λa,x,Λa,y,Λxy,a,Θby); 3.4. Analyzing the construction; References; Coding into H(w2), Together (or Not) with Forcing Axioms. A Survey David Asper o; 1. Main starting questions and some pieces of notation; 2. Results not mentioning forcing axioms; 3. Results mentioning strong forcing axioms; 4. Open questions and some consequences of large cardinal axioms; References; Nonstandard Methods in Ramsey's Theorem for Pairs Chi Tat Chong; 1. Introduction; 2. BE 02 models; References

Prompt Simplicity, Array Computability and Cupping Rod Downey, Noam Greenberg, Joseph S. Miller and Rebecca Weber1. Introduction; 1.1. Notation; 2. PS AC cuppable; 2.1. Construction; 2.2. Veri cations; 3. AC cuppable 6= PS; 3.1. The strategy; 3.2. Construction; 3.3. Veri cation; References; Lowness for Computable Machines Rod Downey, Noam Greenberg, Nenad Mihailovi c and Andr e Nies; 1. Introduction; 2. The Proof; References; A Simpler Short Extenders Forcing | Gap 3 Moti Gitik; 1. The Preparation Forcing; 2. Types of Models; 3. The Main Forcing; Acknowledgment; References

Limit Computability and Constructive Measure Denis R. Hirschfeldt and Sebastiaan A. Terwijn1. Introduction; 2. 0 -dimension; 3. The measure of the low sets; Acknowledgments; References; The Strength of Some Combinatorial Principles Related to Ramsey's Theorem for Pairs Denis R. Hirschfeldt, Carl G. Jockusch, Jr., Bj rn Kjos-Hanssen, Ste en Lempp and Theodore A. Slaman; 1. Introduction; 2. SRT2 implies DNR; 2.1. The argument for w-models; 2.2. The proof-theoretic argument; 3. COH does not imply DNR; 4. Degrees of homogeneous sets for stable colorings; Acknowledgments; References

Absoluteness for Universally Baire Sets and the Uncountable II Ilijas Farah, Richard Ketchersid, Paul Larson and Menachem Magidor

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

9786611955960

9781281955968

1281955965

9789812796554

981279655X