The Notre Dame Lectures

Author: Peter Cholak
Publisher: Cambridge University Press
ISBN: 9781108659932
Release Date: 2017-03-30
Genre: Mathematics

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In the fall of 2000, the logic community at the University of Notre Dame, Indiana hosted Greg Hjorth, Rodney G. Downey, Zoé Chatzidakis and Paola D'Aquino as visiting lecturers. Each of them presented a month-long series of expository lectures at the graduate level. This volume, the eighteenth publication in the Lecture Notes in Logic series, contains refined and expanded versions of those lectures. The four articles are entitled 'Countable models and the theory of Borel equivalence relations', 'Model theory of difference fields', 'Some computability-theoretic aspects of reals and randomness' and 'Weak fragments of Peano arithmetic'.

Logic Colloquium 2006

Author: S. Barry Cooper
Publisher: Cambridge University Press
ISBN: 9780521110815
Release Date: 2009-09-07
Genre: Mathematics

The 2006 proceedings from the Annual European Meeting of the Association for Symbolic Logic, also known as the Logic Colloquium.

Invariant Descriptive Set Theory

Author: Su Gao
Publisher: CRC Press
ISBN: 158488794X
Release Date: 2008-09-03
Genre: Mathematics

Presents Results from a Very Active Area of Research Exploring an active area of mathematics that studies the complexity of equivalence relations and classification problems, Invariant Descriptive Set Theory presents an introduction to the basic concepts, methods, and results of this theory. It brings together techniques from various areas of mathematics, such as algebra, topology, and logic, which have diverse applications to other fields. After reviewing classical and effective descriptive set theory, the text studies Polish groups and their actions. It then covers Borel reducibility results on Borel, orbit, and general definable equivalence relations. The author also provides proofs for numerous fundamental results, such as the Glimm–Effros dichotomy, the Burgess trichotomy theorem, and the Hjorth turbulence theorem. The next part describes connections with the countable model theory of infinitary logic, along with Scott analysis and the isomorphism relation on natural classes of countable models, such as graphs, trees, and groups. The book concludes with applications to classification problems and many benchmark equivalence relations. By illustrating the relevance of invariant descriptive set theory to other fields of mathematics, this self-contained book encourages readers to further explore this very active area of research.

Algorithmic Randomness and Complexity

Author: Rodney G. Downey
Publisher: Springer Science & Business Media
ISBN: 9780387684413
Release Date: 2010-10-29
Genre: Computers

Computability and complexity theory are two central areas of research in theoretical computer science. This book provides a systematic, technical development of "algorithmic randomness" and complexity for scientists from diverse fields.

Computability and Complexity

Author: Adam Day
Publisher: Springer
ISBN: 9783319500621
Release Date: 2016-11-30
Genre: Computers

This Festschrift is published in honor of Rodney G. Downey, eminent logician and computer scientist, surfer and Scottish country dancer, on the occasion of his 60th birthday. The Festschrift contains papers and laudations that showcase the broad and important scientific, leadership and mentoring contributions made by Rod during his distinguished career. The volume contains 42 papers presenting original unpublished research, or expository and survey results in Turing degrees, computably enumerable sets, computable algebra, computable model theory, algorithmic randomness, reverse mathematics, and parameterized complexity, all areas in which Rod Downey has had significant interests and influence. The volume contains several surveys that make the various areas accessible to non-specialists while also including some proofs that illustrate the flavor of the fields.

Proceedings of the International Congress of Mathematicians

Author: Marta Sanz Solé
Publisher: Amer Mathematical Society
ISBN: 3037190221
Release Date: 2006-12
Genre: Mathematics

The International Congress of Mathematicians (ICM) is held every four years. It is a major scientific event, bringing together mathematicians from all over the world and demonstrating the vital role that mathematics play in our society. In particular, the Fields Medals are awarded to recognize outstanding mathematical achievement. At the same time, the International Mathematical Union awards the Nevanlinna Prize for work in the field of theoretical computer science. The proceedings of ICM 2006, published as a three-volume set, present an overview of current research in all areas of mathematics and provide a permanent record the congress. The first volume features the works of Fields Medallists and the Nevanlinna Prize winner, the plenary lectures, and the speeches and pictures of the opening and closing ceremonies and award sessions. The other two volumes present the invited lectures, arranged according to their mathematical subject. Information for our distributors: Distributed within the Americas by the American Mathematical Society. All commerical channel discounts apply.

Model theory of stochastic processes

Author: Sergio Fajardo
Publisher: A K Peters Ltd
ISBN: 1568811675
Release Date: 2002
Genre: Mathematics

This book presents new research in probability theory using ideas from mathematical logic. It is a general study of stochastic processes on adapted probability spaces, employing the concept of similarity of stochastic processes based on the notion of adapted distribution. The authors use ideas from model theory and methods from nonstandard analysis. The construction of spaces with certain richness properties, defined by insights from model theory, becomes easy using nonstandard methods, but remains difficult or impossible without them.

Descriptive Complexity

Author: Neil Immerman
Publisher: Springer Science & Business Media
ISBN: 9781461205395
Release Date: 2012-12-06
Genre: Computers

By virtue of the close relationship between logic and relational databases, it turns out that complexity has important applications to databases such as analyzing the parallel time needed to compute a query, and the analysis of nondeterministic classes. This book is a relatively self-contained introduction to the subject, which includes the necessary background material, as well as numerous examples and exercises.

The Varieties of Religious Experience

Author: William James
Publisher: Modern Library
ISBN: UCAL:B3947882
Release Date: 1902
Genre: Philosophy

William James' series of lectures on religion as it is is apprehended by, and affect, the individual.

Many sorted logic and its applications

Author: Karl Meinke
Publisher: John Wiley & Sons
ISBN: 0471934852
Release Date: 1993-03-09
Genre: Computers

Prominent experts present papers which discuss problems regarding this subject. Coverage includes case studies in the translation of logics for second-order and propositional dynamic logic; many-sorted algebras and equational logic; logical foundations of artificial intelligence along with a variety of methods that exist to encode information; program verification techniques such as Floyd-Hoare, intermittent assertion and temporal logic of programs.

Recursion Theory for Metamathematics

Author: Raymond M. Smullyan
Publisher: Oxford University Press
ISBN: 0195344812
Release Date: 1993-01-28
Genre: Mathematics

This work is a sequel to the author's G?del's Incompleteness Theorems, though it can be read independently by anyone familiar with G?del's incompleteness theorem for Peano arithmetic. The book deals mainly with those aspects of recursion theory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.

Seeking Nature s Logic

Author: David B. Wilson
Publisher: Penn State Press
ISBN: 0271035250
Release Date: 2009
Genre: Science

"Studies the path of natural philosophy (i.e., physics) from Isaac Newton through Scotland into the nineteenth-century background to the modern revolution in physics. Examines how the history of science has been influenced by John Robison and other notable intellectuals of the Scottish Enlightenment"--Provided by publisher.