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ISBN 10: 0691175438 ISBN 13: 9780691175430
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Published by Princeton University Press, 2017
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Published by Princeton University Press, 2017
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Published by Princeton University Press, 2017
ISBN 10: 0691175438 ISBN 13: 9780691175430
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Published by Princeton University Press, 2017
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Published by Princeton University Press, 2017
ISBN 10: 0691175438 ISBN 13: 9780691175430
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Published by Princeton University Press, US, 2017
ISBN 10: 0691175438 ISBN 13: 9780691175430
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Paperback. Condition: New. Asymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view. The differential field of transseries plays a central role in the subject. Besides powers of the variable, these series may contain exponential and logarithmic terms. Over the last thirty years, transseries emerged variously as super-exact asymptotic expansions of return maps of analytic vector fields, in connection with Tarski's problem on the field of reals with exponentiation, and in mathematical physics. Their formal nature also makes them suitable for machine computations in computer algebra systems. This self-contained book validates the intuition that the differential field of transseries is a universal domain for asymptotic differential algebra. It does so by establishing in the realm of transseries a complete elimination theory for systems of algebraic differential equations with asymptotic side conditions. Beginning with background chapters on valuations and differential algebra, the book goes on to develop the basic theory of valued differential fields, including a notion of differential-henselianity.Next, H-fields are singled out among ordered valued differential fields to provide an algebraic setting for the common properties of Hardy fields and the differential field of transseries. The study of their extensions culminates in an analogue of the algebraic closure of a field: the Newton-Liouville closure of an H-field. This paves the way to a quantifier elimination with interesting consequences.
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Published by Princeton University Press, 2017
ISBN 10: 0691175438 ISBN 13: 9780691175430
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Published by Princeton University Press, US, 2017
ISBN 10: 0691175438 ISBN 13: 9780691175430
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Paperback. Condition: New. Asymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view. The differential field of transseries plays a central role in the subject. Besides powers of the variable, these series may contain exponential and logarithmic terms. Over the last thirty years, transseries emerged variously as super-exact asymptotic expansions of return maps of analytic vector fields, in connection with Tarski's problem on the field of reals with exponentiation, and in mathematical physics. Their formal nature also makes them suitable for machine computations in computer algebra systems. This self-contained book validates the intuition that the differential field of transseries is a universal domain for asymptotic differential algebra. It does so by establishing in the realm of transseries a complete elimination theory for systems of algebraic differential equations with asymptotic side conditions. Beginning with background chapters on valuations and differential algebra, the book goes on to develop the basic theory of valued differential fields, including a notion of differential-henselianity.Next, H-fields are singled out among ordered valued differential fields to provide an algebraic setting for the common properties of Hardy fields and the differential field of transseries. The study of their extensions culminates in an analogue of the algebraic closure of a field: the Newton-Liouville closure of an H-field. This paves the way to a quantifier elimination with interesting consequences.
Language: English
Published by Springer-Verlag Berlin and Heidelberg GmbH and Co. KG, DE, 2014
ISBN 10: 3642549357 ISBN 13: 9783642549359
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Published by Princeton University Press, 2017
ISBN 10: 069117542X ISBN 13: 9780691175423
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Published by Princeton University Press, 2017
ISBN 10: 0691175438 ISBN 13: 9780691175430
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Published by Springer, Springer Gabler, 2014
ISBN 10: 3642549357 ISBN 13: 9783642549359
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - Presenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; 2) undecidability in arithmetic; 3) NIP theories; and 4) the model theory of real and complex exponentiation. Young researchers in model theory will particularly benefit from the book, as will more senior researchers in other branches of mathematics.
Taschenbuch. Condition: Neu. Model Theory in Algebra, Analysis and Arithmetic | Cetraro, Italy 2012, Editors: H. Dugald Macpherson, Carlo Toffalori | Lou van den Dries (u. a.) | Taschenbuch | Lecture Notes in Mathematics | vii | Englisch | 2014 | Springer | EAN 9783642549359 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.
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Published by Cambridge University Press CUP, 1998
ISBN 10: 0521598389 ISBN 13: 9780521598385
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Published by Princeton University Press 2017-06-13, 2017
ISBN 10: 0691175438 ISBN 13: 9780691175430
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Published by Cambridge University Press, 1998
ISBN 10: 0521598389 ISBN 13: 9780521598385
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Published by Princeton University Press, US, 2017
ISBN 10: 0691175438 ISBN 13: 9780691175430
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Paperback. Condition: New. Asymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view. The differential field of transseries plays a central role in the subject. Besides powers of the variable, these series may contain exponential and logarithmic terms. Over the last thirty years, transseries emerged variously as super-exact asymptotic expansions of return maps of analytic vector fields, in connection with Tarski's problem on the field of reals with exponentiation, and in mathematical physics. Their formal nature also makes them suitable for machine computations in computer algebra systems. This self-contained book validates the intuition that the differential field of transseries is a universal domain for asymptotic differential algebra. It does so by establishing in the realm of transseries a complete elimination theory for systems of algebraic differential equations with asymptotic side conditions. Beginning with background chapters on valuations and differential algebra, the book goes on to develop the basic theory of valued differential fields, including a notion of differential-henselianity.Next, H-fields are singled out among ordered valued differential fields to provide an algebraic setting for the common properties of Hardy fields and the differential field of transseries. The study of their extensions culminates in an analogue of the algebraic closure of a field: the Newton-Liouville closure of an H-field. This paves the way to a quantifier elimination with interesting consequences.
Kartoniert / Broschiert. Condition: New. Über den AutorMatthias Aschenbrenner is professor of mathematics at the University of California, Los Angeles. Lou van den Dries is professor of mathematics at the University of Illinois, Urbana-Champaign. Joris van.