Finite And Infinite Combinatorics In Sets And Logic

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Finite and Infinite Combinatorics in Sets and Logic

Norbert W Sauer,R.E. Woodrow,B. Sands
Finite and Infinite Combinatorics in Sets and Logic Book PDF

Author : Norbert W Sauer,R.E. Woodrow,B. Sands
Publisher : Springer Science & Business Media
Page : 452 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401120807

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Finite and Infinite Combinatorics in Sets and Logic by Norbert W Sauer,R.E. Woodrow,B. Sands Pdf

This volume contains the accounts of papers delivered at the Nato Advanced Study Institute on Finite and Infinite Combinatorics in Sets and Logic held at the Banff Centre, Alberta, Canada from April 21 to May 4, 1991. As the title suggests the meeting brought together workers interested in the interplay between finite and infinite combinatorics, set theory, graph theory and logic. It used to be that infinite set theory, finite combinatorics and logic could be viewed as quite separate and independent subjects. But more and more those disciplines grow together and become interdependent of each other with ever more problems and results appearing which concern all of those disciplines. I appreciate the financial support which was provided by the N. A. T. O. Advanced Study Institute programme, the Natural Sciences and Engineering Research Council of Canada and the Department of Mathematics and Statistics of the University of Calgary. 11l'te meeting on Finite and Infinite Combinatorics in Sets and Logic followed two other meetings on discrete mathematics held in Banff, the Symposium on Ordered Sets in 1981 and the Symposium on Graphs and Order in 1984. The growing inter-relation between the different areas in discrete mathematics is maybe best illustrated by the fact that many of the participants who were present at the previous meetings also attended this meeting on Finite and Infinite Combinatorics in Sets and Logic.

On Sets and Graphs

Eugenio G. Omodeo,Alberto Policriti,Alexandru I. Tomescu
On Sets and Graphs Book PDF

Author : Eugenio G. Omodeo,Alberto Policriti,Alexandru I. Tomescu
Publisher : Springer
Page : 275 pages
File Size : 47,9 Mb
Release : 2017-05-11
Category : Computers
ISBN : 9783319549811

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On Sets and Graphs by Eugenio G. Omodeo,Alberto Policriti,Alexandru I. Tomescu Pdf

This treatise presents an integrated perspective on the interplay of set theory and graph theory, providing an extensive selection of examples that highlight how methods from one theory can be used to better solve problems originated in the other. Features: explores the interrelationships between sets and graphs and their applications to finite combinatorics; introduces the fundamental graph-theoretical notions from the standpoint of both set theory and dyadic logic, and presents a discussion on set universes; explains how sets can conveniently model graphs, discussing set graphs and set-theoretic representations of claw-free graphs; investigates when it is convenient to represent sets by graphs, covering counting and encoding problems, the random generation of sets, and the analysis of infinite sets; presents excerpts of formal proofs concerning graphs, whose correctness was verified by means of an automated proof-assistant; contains numerous exercises, examples, definitions, problems and insight panels.

Finite and Infinite Sets

A. Hajnal,László Lovász,Vera T. Sós
Finite and Infinite Sets Book PDF

Author : A. Hajnal,László Lovász,Vera T. Sós
Publisher : North Holland
Page : 446 pages
File Size : 47,7 Mb
Release : 1984
Category : Combinatorial analysis
ISBN : OSU:32435022367155

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Finite and Infinite Sets by A. Hajnal,László Lovász,Vera T. Sós Pdf

Colloquia Mathematica Societatis Jânos Bolyai, 37: Finite and Infinite Sets, Vol. I focuses on the principles, operations, and approaches involved in finite and infinite sets. The selection first elaborates on essential chains and squares, cellular automata in trees, almost disjoint families of countable sets, and application of Lovasz local lemma. Discussions focus on deleting operations, number of all and self-dual E-chains, transversality of E-chains and E-squares, and binary E-chains and E-squares. The text then elaborates on induced subgraphs, inverse extremal digraph problems, two Sperne.

Advanced Combinatorics

Louis Comtet
Advanced Combinatorics Book PDF

Author : Louis Comtet
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 43,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401021968

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Advanced Combinatorics by Louis Comtet Pdf

Notwithstanding its title, the reader will not find in this book a systematic account of this huge subject. Certain classical aspects have been passed by, and the true title ought to be "Various questions of elementary combina torial analysis". For instance, we only touch upon the subject of graphs and configurations, but there exists a very extensive and good literature on this subject. For this we refer the reader to the bibliography at the end of the volume. The true beginnings of combinatorial analysis (also called combina tory analysis) coincide with the beginnings of probability theory in the 17th century. For about two centuries it vanished as an autonomous sub ject. But the advance of statistics, with an ever-increasing demand for configurations as well as the advent and development of computers, have, beyond doubt, contributed to reinstating this subject after such a long period of negligence. For a long time the aim of combinatorial analysis was to count the different ways of arranging objects under given circumstances. Hence, many of the traditional problems of analysis or geometry which are con cerned at a certain moment with finite structures, have a combinatorial character. Today, combinatorial analysis is also relevant to problems of existence, estimation and structuration, like all other parts of mathema tics, but exclusively forjinite sets.

Handbook of Set Theory

Matthew Foreman,Akihiro Kanamori
Handbook of Set Theory Book PDF

Author : Matthew Foreman,Akihiro Kanamori
Publisher : Springer Science & Business Media
Page : 2230 pages
File Size : 48,5 Mb
Release : 2009-12-10
Category : Mathematics
ISBN : 9781402057649

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Handbook of Set Theory by Matthew Foreman,Akihiro Kanamori Pdf

Numbers imitate space, which is of such a di?erent nature —Blaise Pascal It is fair to date the study of the foundation of mathematics back to the ancient Greeks. The urge to understand and systematize the mathematics of the time led Euclid to postulate axioms in an early attempt to put geometry on a ?rm footing. With roots in the Elements, the distinctive methodology of mathematics has become proof. Inevitably two questions arise: What are proofs? and What assumptions are proofs based on? The ?rst question, traditionally an internal question of the ?eld of logic, was also wrestled with in antiquity. Aristotle gave his famous syllogistic s- tems, and the Stoics had a nascent propositional logic. This study continued with ?ts and starts, through Boethius, the Arabs and the medieval logicians in Paris and London. The early germs of logic emerged in the context of philosophy and theology. The development of analytic geometry, as exempli?ed by Descartes, ill- tratedoneofthedi?cultiesinherentinfoundingmathematics. Itisclassically phrased as the question ofhow one reconciles the arithmetic with the geom- ric. Arenumbers onetypeofthingand geometricobjectsanother? Whatare the relationships between these two types of objects? How can they interact? Discovery of new types of mathematical objects, such as imaginary numbers and, much later, formal objects such as free groups and formal power series make the problem of ?nding a common playing ?eld for all of mathematics importunate. Several pressures made foundational issues urgent in the 19th century.

Sets and Extensions in the Twentieth Century

Anonim
Sets and Extensions in the Twentieth Century Book PDF

Author : Anonim
Publisher : Elsevier
Page : 878 pages
File Size : 53,6 Mb
Release : 2012-01-24
Category : Mathematics
ISBN : 9780080930664

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Sets and Extensions in the Twentieth Century by Anonim Pdf

Set theory is an autonomous and sophisticated field of mathematics that is extremely successful at analyzing mathematical propositions and gauging their consistency strength. It is as a field of mathematics that both proceeds with its own internal questions and is capable of contextualizing over a broad range, which makes set theory an intriguing and highly distinctive subject. This handbook covers the rich history of scientific turning points in set theory, providing fresh insights and points of view. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in mathematics, the history of philosophy, and any discipline such as computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration Serves as a singular contribution to the intellectual history of the 20th century Contains the latest scholarly discoveries and interpretative insights

The Mathematics of Paul Erdös II

Ronald L. Graham,Jaroslav Nesetril
The Mathematics of Paul Erd s II Book PDF

Author : Ronald L. Graham,Jaroslav Nesetril
Publisher : Springer Science & Business Media
Page : 591 pages
File Size : 46,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642604065

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The Mathematics of Paul Erdös II by Ronald L. Graham,Jaroslav Nesetril Pdf

In 1992, when Paul Erdos was awarded a Doctor Honoris Causa by Charles University in Prague, a small conference was held, bringing together a distin guished group of researchers with interests spanning a variety of fields related to Erdos' own work. At that gathering, the idea occurred to several of us that it might be quite appropriate at this point in Erdos' career to solicit a col lection of articles illustrating various aspects of Erdos' mathematical life and work. The response to our solicitation was immediate and overwhelming, and these volumes are the result. Regarding the organization, we found it convenient to arrange the papers into six chapters, each mirroring Erdos' holistic approach to mathematics. Our goal was not merely a (random) collection of papers but rather a thor oughly edited volume composed in large part by articles explicitly solicited to illustrate interesting aspects of Erdos and his life and work. Each chap ter includes an introduction which often presents a sample of related Erdos' problems "in his own words". All these (sometimes lengthy) introductions were written jointly by editors. We wish to thank the nearly 70 contributors for their outstanding efforts (and their patience). In particular, we are grateful to Bela Bollobas for his extensive documentation of Paul Erdos' early years and mathematical high points (in the first part of this volume); our other authors are acknowledged in their respective chapters. We also want to thank A. Bondy, G. Hahn, I.

Erdös on Graphs

Fan Chung,Ron Graham,At&T Labs
Erd s on Graphs Book PDF

Author : Fan Chung,Ron Graham,At&T Labs
Publisher : CRC Press
Page : 155 pages
File Size : 46,6 Mb
Release : 2020-08-26
Category : Mathematics
ISBN : 9781000108668

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Erdös on Graphs by Fan Chung,Ron Graham,At&T Labs Pdf

This book is a tribute to Paul Erdos, the wandering mathematician once described as the "prince of problem solvers and the absolute monarch of problem posers." It examines the legacy of open problems he left to the world after his death in 1996.

Finite Structures with Few Types

Gregory L. Cherlin,Ehud Hrushovski
Finite Structures with Few Types Book PDF

Author : Gregory L. Cherlin,Ehud Hrushovski
Publisher : Princeton University Press
Page : 201 pages
File Size : 54,7 Mb
Release : 2003
Category : Envelopes (Geometry).
ISBN : 9780691113326

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Finite Structures with Few Types by Gregory L. Cherlin,Ehud Hrushovski Pdf

This book applies model theoretic methods to the study of certain finite permutation groups, the automorphism groups of structures for a fixed finite language with a bounded number of orbits on 4-tuples. Primitive permutation groups of this type have been classified by Kantor, Liebeck, and Macpherson, using the classification of the finite simple groups. Building on this work, Gregory Cherlin and Ehud Hrushovski here treat the general case by developing analogs of the model theoretic methods of geometric stability theory. The work lies at the juncture of permutation group theory, model theory, classical geometries, and combinatorics. The principal results are finite theorems, an associated analysis of computational issues, and an "intrinsic" characterization of the permutation groups (or finite structures) under consideration. The main finiteness theorem shows that the structures under consideration fall naturally into finitely many families, with each family parametrized by finitely many numerical invariants (dimensions of associated coordinating geometries). The authors provide a case study in the extension of methods of stable model theory to a nonstable context, related to work on Shelah's "simple theories." They also generalize Lachlan's results on stable homogeneous structures for finite relational languages, solving problems of effectivity left open by that case. Their methods involve the analysis of groups interpretable in these structures, an analog of Zilber's envelopes, and the combinatorics of the underlying geometries. Taking geometric stability theory into new territory, this book is for mathematicians interested in model theory and group theory.

Combinatorial Set Theory

Lorenz J. Halbeisen
Combinatorial Set Theory Book PDF

Author : Lorenz J. Halbeisen
Publisher : Springer Science & Business Media
Page : 456 pages
File Size : 43,6 Mb
Release : 2011-11-24
Category : Mathematics
ISBN : 1447121732

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Combinatorial Set Theory by Lorenz J. Halbeisen Pdf

This book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lies on the axiom of choice and Ramsey theory. In the second part, the sophisticated technique of forcing, originally developed by Paul Cohen, is explained in great detail. With this technique, one can show that certain statements, like the continuum hypothesis, are neither provable nor disprovable from the axioms of set theory. In the last part, some topics of classical set theory are revisited and further developed in the light of forcing. The notes at the end of each chapter put the results in a historical context, and the numerous related results and the extensive list of references lead the reader to the frontier of research. This book will appeal to all mathematicians interested in the foundations of mathematics, but will be of particular use to graduates in this field.

Graph Symmetry

Gena Hahn,Gert Sabidussi
Graph Symmetry Book PDF

Author : Gena Hahn,Gert Sabidussi
Publisher : Springer Science & Business Media
Page : 434 pages
File Size : 46,6 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401589376

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Graph Symmetry by Gena Hahn,Gert Sabidussi Pdf

The last decade has seen two parallel developments, one in computer science, the other in mathematics, both dealing with the same kind of combinatorial structures: networks with strong symmetry properties or, in graph-theoretical language, vertex-transitive graphs, in particular their prototypical examples, Cayley graphs. In the design of large interconnection networks it was realised that many of the most fre quently used models for such networks are Cayley graphs of various well-known groups. This has spawned a considerable amount of activity in the study of the combinatorial properties of such graphs. A number of symposia and congresses (such as the bi-annual IWIN, starting in 1991) bear witness to the interest of the computer science community in this subject. On the mathematical side, and independently of any interest in applications, progress in group theory has made it possible to make a realistic attempt at a complete description of vertex-transitive graphs. The classification of the finite simple groups has played an important role in this respect.

Algebraic Model Theory

Bradd T. Hart,A. Lachlan,Matthew A. Valeriote
Algebraic Model Theory Book PDF

Author : Bradd T. Hart,A. Lachlan,Matthew A. Valeriote
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 54,7 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401589239

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Algebraic Model Theory by Bradd T. Hart,A. Lachlan,Matthew A. Valeriote Pdf

Recent major advances in model theory include connections between model theory and Diophantine and real analytic geometry, permutation groups, and finite algebras. The present book contains lectures on recent results in algebraic model theory, covering topics from the following areas: geometric model theory, the model theory of analytic structures, permutation groups in model theory, the spectra of countable theories, and the structure of finite algebras. Audience: Graduate students in logic and others wishing to keep abreast of current trends in model theory. The lectures contain sufficient introductory material to be able to grasp the recent results presented.

Directions in Infinite Graph Theory and Combinatorics

R. Diestel
Directions in Infinite Graph Theory and Combinatorics Book PDF

Author : R. Diestel
Publisher : Elsevier
Page : 128 pages
File Size : 50,7 Mb
Release : 2016-06-06
Category : Mathematics
ISBN : 9781483294797

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Directions in Infinite Graph Theory and Combinatorics by R. Diestel Pdf

This book has arisen from a colloquium held at St. John's College, Cambridge, in July 1989, which brought together most of today's leading experts in the field of infinite graph theory and combinatorics. This was the first such meeting ever held, and its aim was to assess the state of the art in the discipline, to consider its links with other parts of mathematics, and to discuss possible directions for future development. This volume reflects the Cambridge meeting in both level and scope. It contains research papers as well as expository surveys of particular areas. Together they offer a comprehensive portrait of infinite graph theory and combinatorics, which should be particularly attractive to anyone new to the discipline.

Advances in Algebra and Model Theory

M Droste,R. Gobel
Advances in Algebra and Model Theory Book PDF

Author : M Droste,R. Gobel
Publisher : CRC Press
Page : 512 pages
File Size : 40,8 Mb
Release : 2019-08-16
Category : Mathematics
ISBN : 9781000717457

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Advances in Algebra and Model Theory by M Droste,R. Gobel Pdf

Contains 25 surveys in algebra and model theory, all written by leading experts in the field. The surveys are based around talks given at conferences held in Essen, 1994, and Dresden, 1995. Each contribution is written in such a way as to highlight the ideas that were discussed at the conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community. The topics include field and ring theory as well as groups, ordered algebraic structure and their relationship to model theory. Several papers deal with infinite permutation groups, abelian groups, modules and their relatives and representations. Model theoretic aspects include quantifier elimination in skew fields, Hilbert's 17th problem, (aleph-0)-categorical structures and Boolean algebras. Moreover symmetry questions and automorphism groups of orders are covered. This work contains 25 surveys in algebra and model theory, each is written in such a way as to highlight the ideas that were discussed at Conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community.

Set Theory

Simon Thomas
Set Theory Book PDF

Author : Simon Thomas
Publisher : American Mathematical Soc.
Page : 184 pages
File Size : 44,6 Mb
Release : 2002-01-01
Category : Mathematics
ISBN : 0821870998

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Set Theory by Simon Thomas Pdf

This volume presents the proceedings from the Mid-Atlantic Mathematical Logic Seminar (MAMLS) conference held in honor of Andras Hajnal at the DIMACS Center, Rutgers University (New Brunswick, NJ). Articles include both surveys and high-level research papers written by internationally recognized experts in the field of set theory. Many of the current active areas of set theory are represented in this volume. It includes research papers on combinatorial set theory, set theoretictopology, descriptive set theory, and set theoretic algebra. There are valuable surveys on combinatorial set theory, fragments of the proper forcing axiom, and the reflection properties of stationary sets. The book also includes an exposition of the ergodic theory of lattices in higher rank semisimpleLie groups-essential reading for anyone who wishes to understand much of the recent work on countable Borel equivalence relations.