Automorphisms of the Lattice of Recursively Enumerable Sets

Automorphisms of the Lattice of Recursively Enumerable Sets
Author :
Publisher : American Mathematical Soc.
Total Pages : 166
Release :
ISBN-10 : 9780821826010
ISBN-13 : 0821826018
Rating : 4/5 (10 Downloads)

Synopsis Automorphisms of the Lattice of Recursively Enumerable Sets by : Peter Cholak

A version of Harrington's [capital Greek]Delta3-automorphism technique for the lattice of recursively enumerable sets is introduced and developed by reproving Soare's Extension Theorem. Then this automorphism technique is used to show two technical theorems: the High Extension Theorem I and the High Extension Theorem II. This is a degree-theoretic technique for constructing both automorphisms of the lattice of r.e. sets and isomorphisms between various substructures of the lattice.

Recursively Enumerable Sets and Degrees

Recursively Enumerable Sets and Degrees
Author :
Publisher : Springer Science & Business Media
Total Pages : 460
Release :
ISBN-10 : 3540152997
ISBN-13 : 9783540152996
Rating : 4/5 (97 Downloads)

Synopsis Recursively Enumerable Sets and Degrees by : Robert I. Soare

..."The book, written by one of the main researchers on the field, gives a complete account of the theory of r.e. degrees. .... The definitions, results and proofs are always clearly motivated and explained before the formal presentation; the proofs are described with remarkable clarity and conciseness. The book is highly recommended to everyone interested in logic. It also provides a useful background to computer scientists, in particular to theoretical computer scientists." Acta Scientiarum Mathematicarum, Ungarn 1988 ..."The main purpose of this book is to introduce the reader to the main results and to the intricacies of the current theory for the recurseively enumerable sets and degrees. The author has managed to give a coherent exposition of a rather complex and messy area of logic, and with this book degree-theory is far more accessible to students and logicians in other fields than it used to be." Zentralblatt für Mathematik, 623.1988

The Incomputable

The Incomputable
Author :
Publisher : Springer
Total Pages : 292
Release :
ISBN-10 : 9783319436692
ISBN-13 : 3319436694
Rating : 4/5 (92 Downloads)

Synopsis The Incomputable by : S. Barry Cooper

This book questions the relevance of computation to the physical universe. Our theories deliver computational descriptions, but the gaps and discontinuities in our grasp suggest a need for continued discourse between researchers from different disciplines, and this book is unique in its focus on the mathematical theory of incomputability and its relevance for the real world. The core of the book consists of thirteen chapters in five parts on extended models of computation; the search for natural examples of incomputable objects; mind, matter, and computation; the nature of information, complexity, and randomness; and the mathematics of emergence and morphogenesis. This book will be of interest to researchers in the areas of theoretical computer science, mathematical logic, and philosophy.

Computational Prospects Of Infinity - Part Ii: Presented Talks

Computational Prospects Of Infinity - Part Ii: Presented Talks
Author :
Publisher : World Scientific
Total Pages : 431
Release :
ISBN-10 : 9789814471527
ISBN-13 : 9814471526
Rating : 4/5 (27 Downloads)

Synopsis Computational Prospects Of Infinity - Part Ii: Presented Talks by : Chi Tat Chong

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.

Computational Prospects of Infinity

Computational Prospects of Infinity
Author :
Publisher : World Scientific
Total Pages : 431
Release :
ISBN-10 : 9789812796554
ISBN-13 : 981279655X
Rating : 4/5 (54 Downloads)

Synopsis Computational Prospects of Infinity by : Chitat Chong

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.

Ordered Sets and Lattices II

Ordered Sets and Lattices II
Author :
Publisher : American Mathematical Soc.
Total Pages : 262
Release :
ISBN-10 : 0821895885
ISBN-13 : 9780821895887
Rating : 4/5 (85 Downloads)

Synopsis Ordered Sets and Lattices II by :

This indispensable reference source contains a wealth of information on lattice theory. The book presents a survey of virtually everything published in the fields of partially ordered sets, semilattices, lattices, and Boolean algebras that was reviewed in Referativnyi Zhurnal Matematika from mid-1982 to the end of 1985. A continuation of a previous volume (the English translation of which was published by the AMS in 1989, as volume 141 in Translations - Series 2), this comprehensive work contains more than 2200 references. Many of the papers covered here were originally published in virtually inaccessible places. The compilation of the volume was directed by Milan Kolibiar of Comenius University at Bratislava and Lev A. Skornyakov of Moscow University. Of interest to mathematicians, as well as to philosophers and computer scientists in certain areas, this unique compendium is a must for any mathematical library.

Mathematical Logic In The 20th Century

Mathematical Logic In The 20th Century
Author :
Publisher : World Scientific
Total Pages : 710
Release :
ISBN-10 : 9789814490191
ISBN-13 : 9814490199
Rating : 4/5 (91 Downloads)

Synopsis Mathematical Logic In The 20th Century by : Gerald E Sacks

This invaluable book is a collection of 31 important — both in ideas and results — papers published by mathematical logicians in the 20th Century. The papers have been selected by Professor Gerald E Sacks. Some of the authors are Gödel, Kleene, Tarski, A Robinson, Kreisel, Cohen, Morley, Shelah, Hrushovski and Woodin.

Computability Theory and Its Applications

Computability Theory and Its Applications
Author :
Publisher : American Mathematical Soc.
Total Pages : 338
Release :
ISBN-10 : 9780821819227
ISBN-13 : 0821819224
Rating : 4/5 (27 Downloads)

Synopsis Computability Theory and Its Applications by : Peter Cholak

This collection of articles presents a snapshot of the status of computability theory at the end of the millennium and a list of fruitful directions for future research. The papers represent the works of experts in the field who were invited speakers at the AMS-IMS-SIAM 1999 Summer Conference on Computability Theory and Applications, which focused on open problems in computability theory and on some related areas in which the ideas, methods, and/or results of computability theory play a role. Some presentations are narrowly focused; others cover a wider area. Topics included from "pure" computability theory are the computably enumerable degrees (M. Lerman), the computably enumerable sets (P. Cholak, R. Soare), definability issues in the c.e. and Turing degrees (A. Nies, R. Shore) and other degree structures (M. Arslanov, S. Badaev and S. Goncharov, P. Odifreddi, A. Sorbi). The topics involving relations between computability and other areas of logic and mathematics are reverse mathematics and proof theory (D. Cenzer and C. Jockusch, C. Chong and Y. Yang, H. Friedman and S. Simpson), set theory (R. Dougherty and A. Kechris, M. Groszek, T. Slaman) and computable mathematics and model theory (K. Ambos-Spies and A. Kucera, R. Downey and J. Remmel, S. Goncharov and B. Khoussainov, J. Knight, M. Peretyat'kin, A. Shlapentokh).