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Author: Su Gao
Publisher: CRC Press
ISBN: 9781584887942
Category : Mathematics
Languages : en
Pages : 392
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Book Description
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
Author: Su Gao
Publisher: CRC Press
ISBN: 9781584887942
Category : Mathematics
Languages : en
Pages : 392
Get Book Here
Book Description
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
Author: Yiannis N. Moschovakis
Publisher: American Mathematical Soc.
ISBN: 0821875361
Category :
Languages : en
Pages : 521
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Book Description
Author: A. S. Kechris
Publisher: Cambridge University Press
ISBN: 9780521358118
Category : Mathematics
Languages : en
Pages : 384
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Book Description
To make this work accessible to logicians as well as set theorists and analysts, classical and modern theory of sets of uniqueness are covered as well as the relevant parts of descriptive set theory.
Author: Richard Mansfield
Publisher: Oxford University Press, USA
ISBN:
Category : Mathematics
Languages : en
Pages : 168
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Book Description
Explores the nature of infinity with a view toward classifying and explaining its mathematical applications. It presents not only the basics of the classical theory, but also an introduction to the many important recent results and methods.
Author: Douglas Edward Miller
Publisher:
ISBN:
Category :
Languages : en
Pages : 304
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Book Description
Author: M. Foreman
Publisher: Cambridge University Press
ISBN: 9780521786447
Category : Mathematics
Languages : en
Pages : 304
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Book Description
This volume, first published in 2000, contains a collection of survey papers providing an introduction for graduate students and researchers in these fields.
Author: Jindřich Zapletal
Publisher: American Mathematical Soc.
ISBN: 0821834509
Category : Mathematics
Languages : en
Pages : 158
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Book Description
Focuses on the relationship between definable forcing and descriptive set theory; the forcing serves as a tool for proving independence of inequalities between cardinal invariants of the continuum.
Author: Arnold W. Miller
Publisher: Cambridge University Press
ISBN: 1316739317
Category : Mathematics
Languages : en
Pages : 136
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Book Description
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 this volume, the fourth publication in the Lecture Notes in Logic series, Miller develops the necessary features of the theory of descriptive sets in order to present a new proof of Louveau's separation theorem for analytic sets. While some background in mathematical logic and set theory is assumed, the material is based on a graduate course given by the author at the University of Wisconsin, Madison, and is thus accessible to students and researchers alike in these areas, as well as in mathematical analysis.
Author: James M. Henle
Publisher: Springer Science & Business Media
ISBN: 1461386802
Category : Mathematics
Languages : en
Pages : 137
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Book Description
This book is designed for use in a one semester problem-oriented course in undergraduate set theory. The combination of level and format is somewhat unusual and deserves an explanation. Normally, problem courses are offered to graduate students or selected undergraduates. I have found, however, that the experience is equally valuable to ordinary mathematics majors. I use a recent modification of R. L. Moore's famous method developed in recent years by D. W. Cohen [1]. Briefly, in this new approach, projects are assigned to groups of students each week. With all the necessary assistance from the instructor, the groups complete their projects, carefully write a short paper for their classmates, and then, in the single weekly class meeting, lecture on their results. While the em phasis is on the student, the instructor is available at every stage to assure success in the research, to explain and critique mathematical prose, and to coach the groups in clear mathematical presentation. The subject matter of set theory is peculiarly appropriate to this style of course. For much of the book the objects of study are familiar and while the theorems are significant and often deep, it is the methods and ideas that are most important. The necessity of rea soning about numbers and sets forces students to come to grips with the nature of proof, logic, and mathematics. In their research they experience the same dilemmas and uncertainties that faced the pio neers.
Author: Sy-David Friedman
Publisher: American Mathematical Soc.
ISBN: 0821894757
Category : Mathematics
Languages : en
Pages : 92
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Book Description
Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper the authors study the generalization where countable is replaced by uncountable. They explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in this generalized setting compared to the classical, countable case. They also draw the connection between the stability theoretic complexity of first-order theories and the descriptive set theoretic complexity of their isomorphism relations. The authors' results suggest that Borel reducibility on uncountable structures is a model theoretically natural way to compare the complexity of isomorphism relations.
