國立虎尾科技大學 |

Slicing the truth = on the computable and reverse mathematics of combinatorial principles /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Slicing the truth/ Denis R. Hirschfeldt ; editors, Chitat Chong ... [et al.]
Reminder of title:	on the computable and reverse mathematics of combinatorial principles /
Author:	Hirschfeldt, Denis Roman.
other author:	Chong, C.-T.
Published:	Singapore ;World Scientific, : 2015.,
Description:	1 online resource (xv, 214 p.)
Subject:	Reverse mathematics. -
Online resource:	http://www.worldscientific.com/worldscibooks/10.1142/9208#t=toc
ISBN:	9789814612623 (electronic bk.)

Slicing the truth = on the computable and reverse mathematics of combinatorial principles /
Hirschfeldt, Denis Roman.

Slicing the truthon the computable and reverse mathematics of combinatorial principles /[electronic resource] :Denis R. Hirschfeldt ; editors, Chitat Chong ... [et al.] - Singapore ;World Scientific,2015. - 1 online resource (xv, 214 p.) - Lecture notes series / Institute for Mathematical Sciences, National University of Singapore ;vol. 28. - Lecture notes series (National University of Singapore. Institute for Mathematical Sciences).

Includes bibliographical references and index.

1. Setting off: An introduction. 1.1. A measure of motivation. 1.2. Computable mathematics. 1.3. Reverse mathematics. 1.4. An overview. 1.5. Further reading -- 2. Gathering our tools: Basic concepts and notation. 2.1. Computability theory. 2.2. Computability theoretic reductions. 2.3. Forcing -- 3. Finding our path: Konig's lemma and computability. 3.1. II[symbol] classes, basis theorems, and PA degrees. 3.2. Versions of Konig's lemma -- 4. Gauging our strength: Reverse mathematics. 4.1. RCA[symbol]. 4.2. Working in RCA[symbol]. 4.3. ACA[symbol]. 4.4. WKL[symbol]. 4.5. [symbol]-models. 4.6. First order axioms. 4.7. Further remarks -- 5. In defense of disarray -- 6. Achieving consensus: Ramsey's theorem. 6.1. Three proofs of Ramsey's theorem. 6.2. Ramsey's theorem and the arithmetic hierarchy. 6.3. RT, ACA[symbol], and the Paris-Harrington theorem. 6.4. Stability and cohesiveness. 6.5. Mathias forcing and cohesive sets. 6.6. Mathias forcing and stable colorings. 6.7. Seetapun's theorem and its extensions. 6.8. Ramsey's theorem and first order axioms. 6.9. Uniformity -- 7. Preserving our power: Conservativity. 7.1. Conservativity over first order systems. 7.2. WKL[symbol] and II[symbol]-conservativity. 7.3. COH and r-II[symbol]-conservativity -- 8. Drawing a map: Five diagrams -- 9. Exploring our surroundings: The world below RT[symbol]. 9.1. Ascending and descending sequences. 9.2. Other combinatorial principles provable from RT[symbol]. 9.3. Atomic models and omitting types -- 10. Charging ahead: Further topics. 10.1. The Dushnik-Miller theorem. 10.2. Linearizing well-founded partial orders. 10.3. The world above ACA[symbol]. 10.4. Still further topics, and a final exercise.

This book is a brief and focused introduction to the reverse mathematics and computability theory of combinatorial principles, an area of research which has seen a particular surge of activity in the last few years. It provides an overview of some fundamental ideas and techniques, and enough context to make it possible for students with at least a basic knowledge of computability theory and proof theory to appreciate the exciting advances currently happening in the area, and perhaps make contributions of their own. It adopts a case-study approach, using the study of versions of Ramsey's Theorem (for colorings of tuples of natural numbers) and related principles as illustrations of various aspects of computability theoretic and reverse mathematical analysis. This book contains many exercises and open questions.

ISBN: 9789814612623 (electronic bk.)Subjects--Topical Terms:

1061150
Reverse mathematics.

LC Class. No.: QA9.25 / .H57 2015eb

Dewey Class. No.: 511/.6

Slicing the truth = on the computable and reverse mathematics of combinatorial principles /
LDR:03718cam a2200301Ia 4500 001 833519
003 OCoLC
005 20151106101121.0
006 m o d
007 cr mn|||||||||
008 160129s2015 si ob 001 0 eng d
020 $a 9789814612623 (electronic bk.)
020 $a 9814612626 (electronic bk.)
020 $z 9789814612616 (hbk.)
020 $z 9814612618 (hbk.)
035 $a (OCoLC)890301359 $z (OCoLC)891387175
035 $a ocn890301359
040 $a N $b eng $c N $d YDXCP $d OTZ $d OSU $d COO $d E7B $d OSU
050 4 $a QA9.25 $b .H57 2015eb
082 0 4 $a 511/.6 $2 23
100 1 $a Hirschfeldt, Denis Roman. $3 1061148
245 1 0 $a Slicing the truth $h [electronic resource] : $b on the computable and reverse mathematics of combinatorial principles / $c Denis R. Hirschfeldt ; editors, Chitat Chong ... [et al.]
260 $a Singapore ; $a Hackensack, NJ : $b World Scientific, $c 2015.
300 $a 1 online resource (xv, 214 p.)
490 1 $a Lecture notes series / Institute for Mathematical Sciences, National University of Singapore ; $v vol. 28
504 $a Includes bibliographical references and index.
505 0 $a 1. Setting off: An introduction. 1.1. A measure of motivation. 1.2. Computable mathematics. 1.3. Reverse mathematics. 1.4. An overview. 1.5. Further reading -- 2. Gathering our tools: Basic concepts and notation. 2.1. Computability theory. 2.2. Computability theoretic reductions. 2.3. Forcing -- 3. Finding our path: Konig's lemma and computability. 3.1. II[symbol] classes, basis theorems, and PA degrees. 3.2. Versions of Konig's lemma -- 4. Gauging our strength: Reverse mathematics. 4.1. RCA[symbol]. 4.2. Working in RCA[symbol]. 4.3. ACA[symbol]. 4.4. WKL[symbol]. 4.5. [symbol]-models. 4.6. First order axioms. 4.7. Further remarks -- 5. In defense of disarray -- 6. Achieving consensus: Ramsey's theorem. 6.1. Three proofs of Ramsey's theorem. 6.2. Ramsey's theorem and the arithmetic hierarchy. 6.3. RT, ACA[symbol], and the Paris-Harrington theorem. 6.4. Stability and cohesiveness. 6.5. Mathias forcing and cohesive sets. 6.6. Mathias forcing and stable colorings. 6.7. Seetapun's theorem and its extensions. 6.8. Ramsey's theorem and first order axioms. 6.9. Uniformity -- 7. Preserving our power: Conservativity. 7.1. Conservativity over first order systems. 7.2. WKL[symbol] and II[symbol]-conservativity. 7.3. COH and r-II[symbol]-conservativity -- 8. Drawing a map: Five diagrams -- 9. Exploring our surroundings: The world below RT[symbol]. 9.1. Ascending and descending sequences. 9.2. Other combinatorial principles provable from RT[symbol]. 9.3. Atomic models and omitting types -- 10. Charging ahead: Further topics. 10.1. The Dushnik-Miller theorem. 10.2. Linearizing well-founded partial orders. 10.3. The world above ACA[symbol]. 10.4. Still further topics, and a final exercise.
520 $a This book is a brief and focused introduction to the reverse mathematics and computability theory of combinatorial principles, an area of research which has seen a particular surge of activity in the last few years. It provides an overview of some fundamental ideas and techniques, and enough context to make it possible for students with at least a basic knowledge of computability theory and proof theory to appreciate the exciting advances currently happening in the area, and perhaps make contributions of their own. It adopts a case-study approach, using the study of versions of Ramsey's Theorem (for colorings of tuples of natural numbers) and related principles as illustrations of various aspects of computability theoretic and reverse mathematical analysis. This book contains many exercises and open questions.
588 $a Description based on print version record.
650 0 $a Reverse mathematics. $3 1061150
650 0 $a Combinatorial analysis. $3 527896
700 1 $a Chong, C.-T. $q (Chi-Tat), $d 1949- $3 908431
830 0 $a Lecture notes series (National University of Singapore. Institute for Mathematical Sciences) $3 1061149
856 4 0 $u http://www.worldscientific.com/worldscibooks/10.1142/9208#t=toc