Classical Descriptive Set Theory, Alexander Kechris

Автор: Miller
Название: Descriptive Set Theory and Forcing
ISBN: 1107168066 ISBN-13(EAN): 9781107168060
Издательство: Cambridge Academ
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Описание: These notes develop the theory of descriptive sets, leading up to a new proof of Louveau`s separation theorem for analytic sets. A first course in mathematical logic and set theory is assumed, making this book suitable for advanced students and researchers.

Автор: Kenneth Ireland; Michael Rosen
Название: A Classical Introduction to Modern Number Theory
ISBN: 038797329X ISBN-13(EAN): 9780387973296
Издательство: Springer
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Описание: Details the historical development of the modern number theory. This text provides wide-ranging coverage of significant results with comparatively elementary proofs. It contains chapters that provide a proof of the Mordel-Weil theorem for elliptic curves over the rational numbers and an overview of progress on the arithmetic of elliptic curves.

Автор: Alexander J. Hahn; J. Dieudonne; O.Timothy O`Meara
Название: The Classical Groups and K-Theory
ISBN: 3642057373 ISBN-13(EAN): 9783642057373
Издательство: Springer
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Описание: It is a great satisfaction for a mathematician to witness the growth and expansion of a theory in which he has taken some part during its early years. When H. Weyl coined the words "classical groups," foremost in his mind were their connections with invariant theory, which his famous book helped to revive. Although his approach in that book was deliberately algebraic, his interest in these groups directly derived from his pioneering study of the special case in which the scalars are real or complex numbers, where for the first time he injected Topology into Lie theory. But ever since the definition of Lie groups, the analogy between simple classical groups over finite fields and simple classical groups over IR or C had been observed, even if the concept of "simplicity" was not quite the same in both cases. With the discovery of the exceptional simple complex Lie algebras by Killing and E. Cartan, it was natural to look for corresponding groups over finite fields, and already around 1900 this was done by Dickson for the exceptional Lie algebras G and E - However, a deep reason for this 2 6 parallelism was missing, and it is only Chevalley who, in 1955 and 1961, discovered that to each complex simple Lie algebra corresponds, by a uniform process, a group scheme (fj over the ring Z of integers, from which, for any field K, could be derived a group (fj(K).

Автор: Pandelis Dodos
Название: Banach Spaces and Descriptive Set Theory: Selected Topics
ISBN: 3642121527 ISBN-13(EAN): 9783642121524
Издательство: Springer
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Описание: Basic Concepts.- The Standard Borel Space of All Separable Banach Spaces.- The ?2 Baire Sum.- Amalgamated Spaces.- Zippin's Embedding Theorem.- The Bourgain-Pisier Construction.- Strongly Bounded Classes of Banach Spaces.

Автор: Melvyn B. Nathanson
Название: Additive Number Theory The Classical Bases
ISBN: 1441928480 ISBN-13(EAN): 9781441928481
Издательство: Springer
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