Effective Mathematics of the Uncountable
Title | Effective Mathematics of the Uncountable PDF eBook |
Author | Noam Greenberg |
Publisher | |
Pages | 207 |
Release | 2013 |
Genre | Electronic books |
ISBN | 9781139892032 |
A comprehensive introduction to eight major approaches to computation on uncountable mathematical domains.
Effective Mathematics of the Uncountable
Title | Effective Mathematics of the Uncountable PDF eBook |
Author | Noam Greenberg |
Publisher | Cambridge University Press |
Pages | 205 |
Release | 2013-10-31 |
Genre | Mathematics |
ISBN | 1107014514 |
A comprehensive introduction to eight major approaches to computation on uncountable mathematical domains.
Effective Mathematics of the Uncountable
Title | Effective Mathematics of the Uncountable PDF eBook |
Author | Noam Greenberg |
Publisher | |
Pages | 197 |
Release | 2013 |
Genre | Computable functions |
ISBN | 9781461953678 |
Slicing The Truth: On The Computable And Reverse Mathematics Of Combinatorial Principles
Title | Slicing The Truth: On The Computable And Reverse Mathematics Of Combinatorial Principles PDF eBook |
Author | Denis R Hirschfeldt |
Publisher | World Scientific |
Pages | 231 |
Release | 2014-07-18 |
Genre | Mathematics |
ISBN | 9814612634 |
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.
Ordinal Computability
Title | Ordinal Computability PDF eBook |
Author | Merlin Carl |
Publisher | Walter de Gruyter GmbH & Co KG |
Pages | 343 |
Release | 2019-09-23 |
Genre | Mathematics |
ISBN | 3110496151 |
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.
Computable Structure Theory
Title | Computable Structure Theory PDF eBook |
Author | Antonio Montalbán |
Publisher | Cambridge University Press |
Pages | 213 |
Release | 2021-06-24 |
Genre | Mathematics |
ISBN | 1108423299 |
Presents main results and techniques in computable structure theory together in a coherent framework for the first time in 20 years.
Induction, Bounding, Weak Combinatorial Principles, and the Homogeneous Model Theorem
Title | Induction, Bounding, Weak Combinatorial Principles, and the Homogeneous Model Theorem PDF eBook |
Author | Denis R. Hirschfeldt |
Publisher | American Mathematical Soc. |
Pages | 114 |
Release | 2017-09-25 |
Genre | Mathematics |
ISBN | 1470426579 |
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.