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During the past 25 years, set theory has developed in several
interesting directions. The most outstanding results cover the
application of sophisticated techniques to problems in analysis,
topology, infinitary combinatorics and other areas of mathematics.
This book contains a selection of contributions, some of which are
expository in nature, embracing various aspects of the latest
developments. Amongst topics treated are forcing axioms and their
applications, combinatorial principles used to construct models,
and a variety of other set theoretical tools including inner
models, partitions and trees. Audience: This book will be of
interest to graduate students and researchers in foundational
problems of mathematics.
This is a collection of articles on set theory written by some of
the participants in
theResearchProgrammeonSetTheoryanditsApplicationsthattookplaceatthe
Centre de Recerca Matem' atica (CRM) in Bellaterra (Barcelona). The
Programme run from September 2003 to July 2004 and included an
international conference on set theory in September 2003, an
advanced course on Ramsey methods in ? analysis in January 2004,
and a joint CRM-ICREA workshop on the foundations of set theory in
June 2004, the latter held in Barcelona. A total of 33 short and
long term visitors from 15 countries participated in the Programme.
This volume consists of two parts, the ?rst containing survey
papers on some of the mainstream areas of set theory, and the
second containing original research papers. All of them are
authored by visitors who took part in the set theory Programme or
by participants in the Programme's activities. The survey papers
cover topics 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 t- ory, de?nable versions of large
cardinals, and selection theory for open covers of topological
spaces. As for the research papers, they range from topics such as
the number of near-coherence classes of ultra?lters, the
consistency strength of bounded forcing axioms,P (?)
combinatorics,someapplicationsof morasses,subgroupsofAbelian ?
Polish groups, adding club subsets of ? with ?nite conditions, the
consistency 2 strength of mutual stationarity, and new axioms of
set theory.
During the past 25 years, set theory has developed in several
interesting directions. The most outstanding results cover the
application of sophisticated techniques to problems in analysis,
topology, infinitary combinatorics and other areas of mathematics.
This book contains a selection of contributions, some of which are
expository in nature, embracing various aspects of the latest
developments. Amongst topics treated are forcing axioms and their
applications, combinatorial principles used to construct models,
and a variety of other set theoretical tools including inner
models, partitions and trees. Audience: This book will be of
interest to graduate students and researchers in foundational
problems of mathematics.
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