Download or read book Classification and Orbit Equivalence Relations written by Greg Hjorth and published by American Mathematical Soc.. This book was released on 2000 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Actions of Polish groups are ubiquitous in mathematics. In certain branches of ergodic theory and functional analysis, one finds a systematic study of the group of measure-preserving transformations and the unitary group. In logic, the analysis of countable models intertwines with results concerning the actions of the infinite symmetric group. This text develops the theory of Polish group actions entirely from scratch, ultimately presenting a coherent theory of the resulting orbit equivalence classes that may allow complete classification by invariants of an indicated form. The book concludes with a criterion for an orbit equivalence relation classifiable by countable structures considered up to isomorphism. This self-contained volume offers a complete treatment of this active area of current research and develops a difficult general theory classifying a class of mathematical objects up to some relevant notion of isomorphism or equivalence.
Download or read book Borel Equivalence Relations written by Vladimir Grigorʹevich Kanoveĭ and published by American Mathematical Soc.. This book was released on 2008 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Over the last 20 years, the theory of Borel equivalence relations and related topics have been very active areas of research in set theory and have important interactions with other fields of mathematics, like ergodic theory and topological dynamics, group theory, combinatorics, functional analysis, and model theory. The book presents, for the first time in mathematical literature, all major aspects of this theory and its applications."--BOOK JACKET.
Download or read book Full Groups Classification and Equivalence Relations written by Benjamin David Miller and published by . This book was released on 2004 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sets and Proofs written by S. Barry Cooper and published by Cambridge University Press. This book was released on 1999-06-17 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: First of two volumes providing a comprehensive guide to mathematical logic.
Download or read book Global Aspects of Ergodic Group Actions written by A. S. Kechris and published by American Mathematical Soc.. This book was released on 2010 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: A study of ergodic, measure preserving actions of countable discrete groups on standard probability spaces. It explores a direction that emphasizes a global point of view, concentrating on the structure of the space of measure preserving actions of a given group and its associated cocycle spaces.
Download or read book Appalachian Set Theory written by James Cummings and published by Cambridge University Press. This book was released on 2012-11-15 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers based on a series of workshops where prominent researchers present exciting developments in set theory to a broad audience.
Download or read book Crossed Products of C Algebras Topological Dynamics and Classification written by Thierry Giordano and published by Springer. This book was released on 2018-08-28 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects the notes of the lectures given at an Advanced Course on Dynamical Systems at the Centre de Recerca Matemàtica (CRM) in Barcelona. The notes consist of four series of lectures. The first one, given by Andrew Toms, presents the basic properties of the Cuntz semigroup and its role in the classification program of simple, nuclear, separable C*-algebras. The second series of lectures, delivered by N. Christopher Phillips, serves as an introduction to group actions on C*-algebras and their crossed products, with emphasis on the simple case and when the crossed products are classifiable. The third one, given by David Kerr, treats various developments related to measure-theoretic and topological aspects of crossed products, focusing on internal and external approximation concepts, both for groups and C*-algebras. Finally, the last series of lectures, delivered by Thierry Giordano, is devoted to the theory of topological orbit equivalence, with particular attention to the classification of minimal actions by finitely generated abelian groups on the Cantor set.
Download or read book Restricted Orbit Equivalence written by Daniel J. Rudolph and published by American Mathematical Soc.. This book was released on 1985 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes develop a theory of restricted orbit equivalence which has as particular examples Ornstein's isomorphism theorem for Bernoulli processes, Dye's orbit equivalence theorem for ergodic processes and the theory of Kakutani equivalence developed by Feldman, Ornstein, Weiss and Katok. A number of results from the Bernoulli theory are shown to be true for any restricted orbit equivalence.
Download or read book Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations written by Greg Hjorth and published by American Mathematical Soc.. This book was released on 2005 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contributes to the theory of Borel equivalence relations, considered up to Borel reducibility, and measures preserving group actions considered up to orbit equivalence. This title catalogs the actions of products of the free group and obtains additional rigidity theorems and relative ergodicity results in this context.
Download or read book Topics in Orbit Equivalence written by Alexander S. Kechris and published by Springer Science & Business Media. This book was released on 2004-08-26 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a self-contained introduction to some topics in orbit equivalence theory, a branch of ergodic theory. The first two chapters focus on hyperfiniteness and amenability. Included here are proofs of Dye's theorem that probability measure-preserving, ergodic actions of the integers are orbit equivalent and of the theorem of Connes-Feldman-Weiss identifying amenability and hyperfiniteness for non-singular equivalence relations. The presentation here is often influenced by descriptive set theory, and Borel and generic analogs of various results are discussed. The final chapter is a detailed account of Gaboriau's recent results on the theory of costs for equivalence relations and groups and its applications to proving rigidity theorems for actions of free groups.
Download or read book The Notre Dame Lectures written by Peter Cholak and published by Cambridge University Press. This book was released on 2017-03-30 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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'.
Download or read book Mathematical Approach To Multilevel Multiscale Health Interventions A Pharmaceutical Industry Decline And Policy Response written by Rodrick Wallace and published by World Scientific. This book was released on 2013-01-28 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, based on published studies, takes a unique perspective on the 30-year collapse of pharmaceutical industry productivity in the search for small molecule “magic bullet” interventions. The relentless escalation of inflation-adjusted cost per approved medicine in the United States — from $200 million in 1950 to $1.2 billion in 2010 — has driven industry giants to, at best, slavish imitation in drug design, and at worst, abandonment of research and embracing of widespread fraud in consumer marketing.The book adapts formalism across a number of disciplines to the strategy for design of mutilevel interventions, focusing first on molecular, cellular, and larger scale examples, and then extending the argument to the simplifications provided by the dominant role of social and cultural structures and processes in individual and population patterns of health and illness.In place of “magic bullets”, we must now apply “magic strategies” that act across both the scale and level of organization. This book provides an introductory roadmap to the new tools that will be needed for the design of such strategies./a
Download or read book Invariant Descriptive Set Theory written by Su Gao and published by CRC Press. This book was released on 2008-09-03 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents Results from a Very Active Area of ResearchExploring 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 mathem
Download or read book Rigidity in Dynamics and Geometry written by Marc Burger and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of proceedings is an offspring of the special semester Ergodic Theory, Geometric Rigidity and Number Theory which was held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK, from Jan uary until July, 2000. Beside the activities during the semester, there were workshops held in January, March and July, the first being of introductory nature with five short courses delivered over a week. Although the quality of the workshops was excellent throughout the semester, the idea of these proceedings came about during the March workshop, which is hence more prominently represented, The format of the volume has undergone many changes, but what has remained untouched is the enthusiasm of the contributors since the onset of the project: suffice it to say that even though only two months elapsed between the time we contacted the potential authors and the deadline to submit the papers, the deadline was respected in the vast majority of the cases. The scope of the papers is not completely uniform throughout the volume, although there are some points in common. We asked the authors to write papers keeping in mind the idea that they should be accessible to students. At the same time, we wanted the papers not to be a summary of results that appeared somewhere else.
Download or read book Transactions on Computational Systems Biology XIII written by Ralph-Johan Back and published by Springer. This book was released on 2011-05-05 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: The LNCS journal Transactions on Computational Systems Biology is devoted to inter- and multidisciplinary research in the fields of computer science and life sciences and supports a paradigmatic shift in the techniques from computer and information science to cope with the new challenges arising from the systems oriented point of view of biological phenomena. This, the 13th Transactions on Computational Systems Biology volume, guest edited by Ralph-Johan Back, Ion Petre, and Erik de Vink, focuses on Computational Models for Cell Processes and features a number of carefully selected and enhanced contributions initially presented at the CompMod workshop, which took place in Eindhoven, The Netherlands, in November 2009. From different points of view and following various approaches, the papers cover a wide range of topics in systems biology, addressing the dynamics and the computational principles of this emerging field.
Download or read book Analysis and Logic written by C. Ward Henson and published by Cambridge University Press. This book was released on 2002 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises articles from four outstanding researchers who work at the cusp of analysis and logic. The emphasis is on active research topics; many results are presented that have not been published before and open problems are formulated. Considerable effort has been made by the authors to integrate their articles and make them accessible to mathematicians new to the area.
Download or read book Ergodic Theory written by Cesar E. Silva and published by Springer Nature. This book was released on 2023-07-31 with total page 707 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, covers recent developments in classical areas of ergodic theory, including the asymptotic properties of measurable dynamical systems, spectral theory, entropy, ergodic theorems, joinings, isomorphism theory, recurrence, nonsingular systems. It enlightens connections of ergodic theory with symbolic dynamics, topological dynamics, smooth dynamics, combinatorics, number theory, pressure and equilibrium states, fractal geometry, chaos. In addition, the new edition includes dynamical systems of probabilistic origin, ergodic aspects of Sarnak's conjecture, translation flows on translation surfaces, complexity and classification of measurable systems, operator approach to asymptotic properties, interplay with operator algebras
