Effective Mathematics Of The Uncountable
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Author |
: Noam Greenberg |
Publisher |
: Cambridge University Press |
Total Pages |
: 205 |
Release |
: 2013-10-31 |
ISBN-10 |
: 9781107512009 |
ISBN-13 |
: 110751200X |
Rating |
: 4/5 (09 Downloads) |
Synopsis Effective Mathematics of the Uncountable by : Noam Greenberg
Classical computable model theory is most naturally concerned with countable domains. There are, however, several methods – some old, some new – that have extended its basic concepts to uncountable structures. Unlike in the classical case, however, no single dominant approach has emerged, and different methods reveal different aspects of the computable content of uncountable mathematics. This book contains introductions to eight major approaches to computable uncountable mathematics: descriptive set theory; infinite time Turing machines; Blum-Shub-Smale computability; Sigma-definability; computability theory on admissible ordinals; E-recursion theory; local computability; and uncountable reverse mathematics. This book provides an authoritative and multifaceted introduction to this exciting new area of research that is still in its early stages. It is ideal as both an introductory text for graduate and advanced undergraduate students and a source of interesting new approaches for researchers in computability theory and related areas.
Author |
: Noam Greenberg |
Publisher |
: |
Total Pages |
: 207 |
Release |
: 2013 |
ISBN-10 |
: 1139892037 |
ISBN-13 |
: 9781139892032 |
Rating |
: 4/5 (37 Downloads) |
Synopsis Effective Mathematics of the Uncountable by : Noam Greenberg
A comprehensive introduction to eight major approaches to computation on uncountable mathematical domains.
Author |
: Noam Greenberg |
Publisher |
: Cambridge University Press |
Total Pages |
: 205 |
Release |
: 2013-10-31 |
ISBN-10 |
: 9781107014510 |
ISBN-13 |
: 1107014514 |
Rating |
: 4/5 (10 Downloads) |
Synopsis Effective Mathematics of the Uncountable by : Noam Greenberg
A comprehensive introduction to eight major approaches to computation on uncountable mathematical domains.
Author |
: Noam Greenberg |
Publisher |
: |
Total Pages |
: 197 |
Release |
: 2013 |
ISBN-10 |
: 1107521181 |
ISBN-13 |
: 9781107521186 |
Rating |
: 4/5 (81 Downloads) |
Synopsis Effective Mathematics of the Uncountable by : Noam Greenberg
Classical computable model theory is most naturally concerned with countable domains. There are, however, several methods - some old, some new - that have extended its basic concepts to uncountable structures. Unlike in the classical case, however, no single dominant approach has emerged, and different methods reveal different aspects of the computable content of uncountable mathematics. This book contains introductions to eight major approaches to computable uncountable mathematics: descriptive set theory; infinite time Turing machines; Blum-Shub-Smale computability; Sigma-definability; computability theory on admissible ordinals; E-recursion theory; local computability; and uncountable reverse mathematics. This book provides an authoritative and multifaceted introduction to this exciting new area of research that is still in its early stages. It is ideal as both an introductory text for graduate and advanced undergraduate students, and a source of interesting new approaches for researchers in computability theory and related areas.--
Author |
: Denis R Hirschfeldt |
Publisher |
: World Scientific |
Total Pages |
: 231 |
Release |
: 2014-07-18 |
ISBN-10 |
: 9789814612630 |
ISBN-13 |
: 9814612634 |
Rating |
: 4/5 (30 Downloads) |
Synopsis Slicing The Truth: On The Computable And Reverse Mathematics Of Combinatorial Principles by : Denis R Hirschfeldt
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.
Author |
: Merlin Carl |
Publisher |
: Walter de Gruyter GmbH & Co KG |
Total Pages |
: 343 |
Release |
: 2019-09-23 |
ISBN-10 |
: 9783110496154 |
ISBN-13 |
: 3110496151 |
Rating |
: 4/5 (54 Downloads) |
Synopsis Ordinal Computability by : Merlin Carl
Ordinal Computability discusses models of computation obtained by generalizing classical models, such as Turing machines or register machines, to transfinite working time and space. In particular, recognizability, randomness, and applications to other areas of mathematics are covered.
Author |
: Antonio Montalbán |
Publisher |
: Cambridge University Press |
Total Pages |
: 213 |
Release |
: 2021-06-24 |
ISBN-10 |
: 9781108423298 |
ISBN-13 |
: 1108423299 |
Rating |
: 4/5 (98 Downloads) |
Synopsis Computable Structure Theory by : Antonio Montalbán
Presents main results and techniques in computable structure theory together in a coherent framework for the first time in 20 years.
Author |
: Denis R. Hirschfeldt |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 114 |
Release |
: 2017-09-25 |
ISBN-10 |
: 9781470426576 |
ISBN-13 |
: 1470426579 |
Rating |
: 4/5 (76 Downloads) |
Synopsis Induction, Bounding, Weak Combinatorial Principles, and the Homogeneous Model Theorem by : Denis R. Hirschfeldt
Goncharov and Peretyat'kin independently gave necessary and sufficient conditions for when a set of types of a complete theory is the type spectrum of some homogeneous model of . Their result can be stated as a principle of second order arithmetic, which is called the Homogeneous Model Theorem (HMT), and analyzed from the points of view of computability theory and reverse mathematics. Previous computability theoretic results by Lange suggested a close connection between HMT and the Atomic Model Theorem (AMT), which states that every complete atomic theory has an atomic model. The authors show that HMT and AMT are indeed equivalent in the sense of reverse mathematics, as well as in a strong computability theoretic sense and do the same for an analogous result of Peretyat'kin giving necessary and sufficient conditions for when a set of types is the type spectrum of some model.
Author |
: Arnold Beckmann |
Publisher |
: Springer |
Total Pages |
: 388 |
Release |
: 2016-06-13 |
ISBN-10 |
: 9783319401898 |
ISBN-13 |
: 3319401890 |
Rating |
: 4/5 (98 Downloads) |
Synopsis Pursuit of the Universal by : Arnold Beckmann
This book constitutes the refereed proceedings of the 12th Conference on Computability in Europe, CiE 2016, held in Paris, France, in June/July 2016. The 18 revised full papers and 19 invited papers and invited extended abstracts were carefully reviewed and selected from 40 submissions. The conference CiE 2016 has six special sessions – two sessions, cryptography and information theory and symbolic dynamics, are organized for the first time in the conference series. In addition to this new developments in areas frequently covered in the CiE conference series were addressed in the following sessions: computable and constructive analysis; computation in biological systems; history and philosophy of computing; weak arithmetic.
Author |
: Paola Bonizzoni |
Publisher |
: Springer |
Total Pages |
: 462 |
Release |
: 2013-06-03 |
ISBN-10 |
: 9783642390531 |
ISBN-13 |
: 3642390536 |
Rating |
: 4/5 (31 Downloads) |
Synopsis The Nature of Computation: Logic, Algorithms, Applications by : Paola Bonizzoni
This book constitutes the refereed proceedings of the 9th Conference on Computability in Europe, CiE 2013, held in Milan, Italy, in July 2013. The 48 revised papers presented together with 1 invited lecture and 2 tutorials were carefully reviewed and selected with an acceptance rate of under 31,7%. Both the conference series and the association promote the development of computability-related science, ranging over mathematics, computer science and applications in various natural and engineering sciences such as physics and biology, and also including the promotion of related non-scientific fields such as philosophy and history of computing.