Stevo Todorcevic's Books

Ramsey Methods in Analysis

By: Spiros A. Argyros,Stevo Todorcevic

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This book contains two sets of notes prepared for the Advanced Course on R- sey Methods in Analysis given at the Centre de Recerca Matem` atica in January 2004, as part of its year-long research programme on Set Theory and its Appli- tions. The common goal of the two sets of notes is to help young mathematicians enter a very active area of research lying on the borderline between analysis and combinatorics. The solution of the distortion problem for the Hilbert space, the unconditional basic sequence problem for Banach spaces, and the Banach ho- geneous space problem are samples of the most important recent advances in this area, and our two sets of notes will give some account of this. But our main goal was to try to expose the general principles and methods that lie hidden behind and are most likely useful for further developments. The goal of the ?rst set of notes is to describe a general method of building norms with desired properties, a method that is clearly relevant when testing any sort of intuition about the in?nite-dimensional geometry of Banach spaces. The goal of the second set of notes is to expose Ramsey-theoretic methods relevant for describing the rough structure present in this sort of geometry. We would like to thank the coordinator of the Advanced Course, Joan Ba- ria, and the director of the CRM, Manuel Castellet, for giving us this challenging but rewarding opportunity. Part A SaturatedandConditional StructuresinBanachSpaces SpirosA.

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258

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3764373601

ISBN 13

9783764373603

Introduction to Ramsey Spaces (AM-174)

By: Stevo Todorcevic

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Introduction to Ramsey Spaces (AM-174)

By: Stevo Todorcevic

Ramsey theory is a fast-growing area of combinatorics with deep connections to other fields of mathematics such as topological dynamics, ergodic theory, mathematical logic, and algebra. The area of Ramsey theory dealing with Ramsey-type phenomena in higher dimensions is particularly useful. Introduction to Ramsey Spaces presents in a systematic way a method for building higher-dimensional Ramsey spaces from basic one-dimensional principles. It is the first book-length treatment of this area of Ramsey theory, and emphasizes applications for related and surrounding fields of mathematics, such as set theory, combinatorics, real and functional analysis, and topology. In order to facilitate accessibility, the book gives the method in its axiomatic form with examples that cover many important parts of Ramsey theory both finite and infinite. An exciting new direction for combinatorics, this book will interest graduate students and researchers working in mathematical subdisciplines requiring the mastery and practice of high-dimensional Ramsey theory.

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296

Publisher

Princeton University Press

Published Date

ISBN 10

1400835402

ISBN 13

9781400835409

Topics in Topology

By: Stevo Todorcevic

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Topics in Topology

By: Stevo Todorcevic

The book describes some interactions of topology with other areas of mathematics and it requires only basic background. The first chapter deals with the topology of pointwise convergence and proves results of Bourgain, Fremlin, Talagrand and Rosenthal on compact sets of Baire class-1 functions. In the second chapter some topological dynamics of beta-N and its applications to combinatorial number theory are presented. The third chapter gives a proof of the Ivanovskii-Kuzminov-Vilenkin theorem that compact groups are dyadic. The last chapter presents Marjanovic's classification of hyperspaces of compact metric zerodimensional spaces.

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Page Count

161

Publisher

Springer

Published Date

ISBN 10

3540683380

ISBN 13

9783540683384

Notes On Forcing Axioms

By: Stevo Todorcevic

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Notes On Forcing Axioms

By: Stevo Todorcevic

In the mathematical practice, the Baire category method is a tool for establishing the existence of a rich array of generic structures. However, in mathematics, the Baire category method is also behind a number of fundamental results such as the Open Mapping Theorem or the Banach-Steinhaus Boundedness Principle. This volume brings the Baire category method to another level of sophistication via the internal version of the set-theoretic forcing technique. It is the first systematic account of applications of the higher forcing axioms with the stress on the technique of building forcing notions rather than on the relationship between different forcing axioms or their consistency strengths.

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234

Publisher

World Scientific

Published Date

ISBN 10

9814571598

ISBN 13

9789814571593

Partition Problems in Topology

By: Stevo Todorcevic

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Partition Problems in Topology

By: Stevo Todorcevic

This book presents results on the case of the Ramsey problem for the uncountable: When does a partition of a square of an uncountable set have an uncountable homogeneous set? This problem most frequently appears in areas of general topology, measure theory, and functional analysis. Building on his solution of one of the two most basic partition problems in general topology, the ``S-space problem,'' the author has unified most of the existing results on the subject and made many improvements and simplifications. The first eight sections of the book require basic knowldege of naive set theory at the level of a first year graduate or advanced undergraduate student. The book may also be of interest to the exclusively set-theoretic reader, for it provides an excellent introduction to the subject of forcing axioms of set theory, such as Martin's axiom and the Proper forcing axiom.

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Page Count

130

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821850911

ISBN 13

9780821850916

Introduction to Ramsey Spaces (AM-174)

By: Stevo Todorcevic

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Introduction to Ramsey Spaces (AM-174)

By: Stevo Todorcevic

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296

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Princeton University Press

Published Date

ISBN 10

1400835402

ISBN 13

9781400835409

Partition Problems in Topology

By: Stevo Todorcevic

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Partition Problems in Topology

By: Stevo Todorcevic

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130

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American Mathematical Soc.

Published Date

ISBN 10

0821850911

ISBN 13

9780821850916

Set Theory

Centre de Recerca Matemàtica Barcelona, 2003-2004

By: Joan Bagaria,Stevo Todorcevic

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Set Theory

Centre de Recerca Matemàtica Barcelona, 2003-2004

By: Joan Bagaria,Stevo Todorcevic

Contains survey papers on some of the mainstream areas of set theory and research. This book covers topics such as Omega-logic, applications of set theory to lattice theory and Boolean algebras, real-valued measurable cardinals, complexity of sets and relations in continuum theory, weak subsystems of axiomatic set theory, and more.

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Page Count

408

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3764376929

ISBN 13

9783764376925

Ramsey Methods in Analysis

By: Spiros A. Argyros,Stevo Todorcevic

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Ramsey Methods in Analysis

By: Spiros A. Argyros,Stevo Todorcevic

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258

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Springer Science & Business Media

Published Date

ISBN 10

3764373601

ISBN 13

9783764373603

Ramsey Methods in Analysis

By: Spiros Argyros,Stevo Todorcevic

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Ramsey Methods in Analysis

By: Spiros Argyros,Stevo Todorcevic

We also apply the Nash-Williams theory of fronts and barriers in the study of Cezaro summability and unconditionality present in basic sequences inside a given Banach space. We further provide a detailed exposition of the block-Ramsey theory and its recent deep adjustments relevant to the Banach space theory due to Gowers."--BOOK JACKET.

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Page Count

257

Publisher

Birkhauser

Published Date

ISBN 10

0817672648

ISBN 13

9780817672645

Book's by Stevo Todorcevic

Ramsey Methods in Analysis

Ramsey Methods in Analysis

Introduction to Ramsey Spaces (AM-174)

Introduction to Ramsey Spaces (AM-174)

Topics in Topology

Topics in Topology

Notes On Forcing Axioms

Notes On Forcing Axioms

Partition Problems in Topology

Partition Problems in Topology

Introduction to Ramsey Spaces (AM-174)

Introduction to Ramsey Spaces (AM-174)

Partition Problems in Topology

Partition Problems in Topology

Set Theory

Set Theory

Ramsey Methods in Analysis

Ramsey Methods in Analysis

Ramsey Methods in Analysis

Ramsey Methods in Analysis

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