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  • 1
    Book
    Book
    Analysis and logic / (2002)
    New York :Cambridge University Press,
    Details
    UID:
    almafu_BV014509869
    Format: XIV, 267 S.
    Edition: 1. publ.
    ISBN: 0-521-64861-0
    Series Statement: London Mathematical Society lecture note series 262
    Note: Includes bibliographical references and index
    Language: English
    Subjects: Mathematics
    RVK:
    SI 320
    RVK:
    SK 130
    Keywords: Mathematische Logik ; Modelltheorie ; Analysis ; Konferenzschrift
    URL: Table of contents
    URL: Publisher description
    URL: http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009884580&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
    URL: Table of contents
    URL: Publisher description
    URL: Inhaltsverzeichnis
    URL: Table of contents
    URL: Publisher description
    URL: http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009884580&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
    URL: Inhaltsverzeichnis
    URL: Inhaltstext
    URL: http://www.loc.gov/catdir/toc/cam031/2002071488.html
    URL: http://www.loc.gov/catdir/description/cam0210/2002071488.html
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  • 2
    Book
    Book
    First order topology (1977)
    Warszawa : PWN
    Details
    UID:
    b3kat_BV005828518
    Format: 44 S.
    Series Statement: Dissertationes mathematicae. 143.
    Language: Undetermined
    Subjects: Mathematics
    RVK:
    SI 390
    Keywords: Topologische Modelltheorie ; Topologischer Raum
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  • 3
    Online Resource
    Online Resource
    Nonstandard Analysis : Theory and Applications (1997)
    Dordrecht : Springer Netherlands
    Details
    UID:
    b3kat_BV042416074
    Format: 1 Online-Ressource (XIV, 366 p)
    ISBN: 9789401155441 , 9789401063357
    Series Statement: NATO ASI Series, Series C: Mathematical and Physical Sciences 493
    Note: 1 More than thirty years after its discovery by Abraham Robinson , the ideas and techniques of Nonstandard Analysis (NSA) are being applied across the whole mathematical spectrum,as well as constituting an important field of research in their own right. The current methods of NSA now greatly extend Robinson's original work with infinitesimals. However, while the range of applications is broad, certain fundamental themes recur. The nonstandard framework allows many informal ideas (that could loosely be described as idealisation) to be made precise and tractable. For example, the real line can (in this framework) be treated simultaneously as both a continuum and a discrete set of points; and a similar dual approach can be used to link the notions infinite and finite, rough and smooth. This has provided some powerful tools for the research mathematician - for example Loeb measure spaces in stochastic analysis and its applications, and nonstandard hulls in Banach spaces. The achievements of NSA can be summarised under the headings (i) explanation - giving fresh insight or new approaches to established theories; (ii) discovery - leading to new results in many fields; (iii) invention - providing new, rich structures that are useful in modelling and representation, as well as being of interest in their own right. The aim of the present volume is to make the power and range of applicability of NSA more widely known and available to research mathematicians
    Language: English
    Keywords: Nonstandard-Analysis ; Konferenzschrift
    DOI: 10.1007/978-94-011-5544-1
    URL: Volltext
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    Online Access
    Open Access Request
    TU Berlin
  • 4
    Online Resource
    Online Resource
    Nonstandard Analysis : Theory and Applications (1997)
    Dordrecht :Springer Netherlands :
    Details
    UID:
    almahu_9949199204902882
    Format: XIV, 366 p. , online resource.
    Edition: 1st ed. 1997.
    ISBN: 9789401155441
    Series Statement: Nato Science Series C:, Mathematical and Physical Sciences ; 493
    Content: 1 More than thirty years after its discovery by Abraham Robinson , the ideas and techniques of Nonstandard Analysis (NSA) are being applied across the whole mathematical spectrum,as well as constituting an im­ portant field of research in their own right. The current methods of NSA now greatly extend Robinson's original work with infinitesimals. However, while the range of applications is broad, certain fundamental themes re­ cur. The nonstandard framework allows many informal ideas (that could loosely be described as idealisation) to be made precise and tractable. For example, the real line can (in this framework) be treated simultaneously as both a continuum and a discrete set of points; and a similar dual ap­ proach can be used to link the notions infinite and finite, rough and smooth. This has provided some powerful tools for the research mathematician - for example Loeb measure spaces in stochastic analysis and its applications, and nonstandard hulls in Banach spaces. The achievements of NSA can be summarised under the headings (i) explanation - giving fresh insight or new approaches to established theories; (ii) discovery - leading to new results in many fields; (iii) invention - providing new, rich structures that are useful in modelling and representation, as well as being of interest in their own right. The aim of the present volume is to make the power and range of appli­ cability of NSA more widely known and available to research mathemati­ cians.
    Note: Foundations of Nonstandard Analysis A Gentle Introduction to Nonstandard Extensions -- 1 Introduction -- 2 Nonstandard Extensions -- 3 Logical Formulas -- 4 Nonstandard Extensions of Multisets -- 5 Nonstandard Extensions of the Multiset (X, P(X)) -- 6 Superstructures -- 7 Saturation -- Nonstandard Real Analysis -- 1 Introduction -- 2 Basic Properties of *? -- 3 Sequences and Series -- 4 Continuity -- 5 Differentiation -- 6 Riemann Integration -- 7 Topology on ? -- 8 Using Internal Subsets of *? -- 9 An Application: Differential Equations -- Nonstandard Analysis and Topology -- 1 Metric and Topological Spaces -- 2 Continuous Mappings -- 3 Convergence -- 4 More on Topologies -- 5 Compact Spaces -- 6 Product Spaces -- 7 Restricted or Relative Topologies -- 8 Uniform Continuity on Metric Spaces -- 9 Nonstandard Hulls -- 10 Compactifications -- 11 More Exercises -- Loeb Measure and Probability -- 1 Introduction -- 2 Finite Loeb Measure -- 3 Constructing Standard Measures -- 4 Representing Standard Measures -- 5 Measurable Functions -- 6 Integration Theory -- 7 Probability Theory -- 8 Advertisement -- 9 Exercises -- An Introduction to Nonstandard Functional Analysis -- 1 Elementary Nonstandard Analysis of Normed Linear Spaces -- 2 Advanced Theory of Banach Spaces -- 3 Elementary Theory of Linear Operators -- 4 Spectral Theory of Bounded Operators -- 5 Applications of Nonstandard Spectral Theory -- 6 Closed Operators -- Applications of Nonstandard Analysis in Ordinary Differential Equations -- 1 Introduction -- 2 Tools in NSA -- 3 Differential Equations and Recursive Sequences -- 4 Regular Perturbations -- 5 Example -- 6 Dynamical Systems: Notions of Stability -- 7 Singular Perturbations -- Better Nonstandard Universes with Applications -- 1 Introduction -- 2 The Isomorphism Property -- 3 The Special Model Axiom and Full Saturation -- 4 The ?-Bolzano-Weierstrass Property -- Internal Martingales and Stochastic Integration -- 1 Hyperfinite Probability Spaces -- 2 Poisson Processes -- 3 Brownian Motion -- 4 Internal Martingales -- 5 Doob's Inequality -- 6 Quadratic Variation -- 7 Standard Parts -- 8 S-continuity -- 9 Stochastic Integration -- 10 Itô's Formula -- 11 Lévy's Characterization of Brownian Motion -- 12 Connections to Standard Theory -- 13 Stochastic Integrals in Higher Dimensions -- 14 Stochastic Differential Equations -- 15 Brownian Local Time -- 16 The Infinite Dimensional Ornstein-Uhlenbeck Process -- Stochastic Differential Equations with Extra Properties -- 1 Introduction -- 2 Spaces of Stochastic Processes -- 3 Solutions of Stochastic Differential Equations -- 4 Solutions which are Markov Processes -- 5 A Fixed Point Theorem -- 6 Stochastic Differential Equations with Nondegenerate Coefficients -- Hyperfinite Mathematical Finance -- 1 Introduction -- 2 Finite Market Models -- 3 Pricing Options in a Hyperfinite CRR Model -- 4 Hyperfinite Trading Strategies -- 5 Convergence of Prices and Strategies -- 6 Further Developments -- Applications of Nsa to Mathematical Physics -- 1 A Kinetic Inequality -- 2 The Time Asymptotic Behaviour for Certain Rarefied Gases when the Incoming Fluxes at the Boundary are Given -- 3 On Semiclassical Limits for the Schrödinger Equation -- A Nonstandard Approach to Hydromechanics Navier-Stokes Equations -- 1 Introduction -- 2 Deterministic Navier-Stokes Equations -- 3 Statistical Solutions -- 4 Stochastic Equations -- 5 Some Open Problems.
    In: Springer Nature eBook
    Additional Edition: Printed edition: ISBN 9789401063357
    Additional Edition: Printed edition: ISBN 9780792345862
    Additional Edition: Printed edition: ISBN 9789401155458
    Language: English
    DOI: 10.1007/978-94-011-5544-1
    URL: https://doi.org/10.1007/978-94-011-5544-1
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  • 5
    Online Resource
    Online Resource
    Analysis and logic / (2002)
    Cambridge :Cambridge University Press,
    Details
    UID:
    almahu_9948233757302882
    Format: 1 online resource (xiv, 267 pages) : , digital, PDF file(s).
    ISBN: 9781107360006 (ebook)
    Series Statement: London Mathematical Society lecture note series ; 262
    Content: This volume comprises articles from four outstanding researchers who work at the cusp of analysis and logic. The emphasis is on active research topics; many results are presented that have not been published before and open problems are formulated. Considerable effort has been made by the authors to integrate their articles and make them accessible to mathematicians new to the area.
    Note: Title from publisher's bibliographic system (viewed on 05 Oct 2015). , Ultraproducts in Analysis / , Actions of Polish Groups and Classification Problems / , On Subspaces, Asymptotic Structure, and Distortion of Banach Spaces; Connections with Logic /
    Additional Edition: Print version: ISBN 9780521648615
    Language: English
    URL: https://doi.org/10.1017/CBO9781107360006
    Library Location Call Number Volume/Issue/Year Availability
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    Online Resource
    HU Berlin
  • 6
    Online Resource
    Online Resource
    Analysis and logic / (2002)
    Cambridge, U.K. ; : Cambridge University Press,
    Details
    UID:
    almafu_9959242960002883
    Format: 1 online resource (xiv, 267 pages) : , digital, PDF file(s).
    ISBN: 1-139-88249-X , 1-107-10351-7 , 1-139-14603-3 , 0-511-06627-9 , 0-511-06840-9 , 1-107-09216-7 , 1-107-36000-5
    Series Statement: London Mathematical Society lecture note series ;
    Content: This volume comprises articles from four outstanding researchers who work at the cusp of analysis and logic. The emphasis is on active research topics; many results are presented that have not been published before and open problems are formulated. Considerable effort has been made by the authors to integrate their articles and make them accessible to mathematicians new to the area.
    Note: Title from publisher's bibliographic system (viewed on 05 Oct 2015). , Ultraproducts in Analysis / , Actions of Polish Groups and Classification Problems / , On Subspaces, Asymptotic Structure, and Distortion of Banach Spaces; Connections with Logic / , English
    Additional Edition: ISBN 1-299-70717-3
    Additional Edition: ISBN 0-521-64861-0
    Language: English
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    Online Resource
    FU Berlin
  • 7
    Online Resource
    Online Resource
    Analysis and logic (2002)
    Cambridge : Cambridge University Press
    Details
    UID:
    gbv_883346303
    Format: 1 Online-Ressource (xiv, 267 pages) , digital, PDF file(s).
    ISBN: 9781107360006
    Series Statement: London Mathematical Society lecture note series 262
    Content: This volume comprises articles from four outstanding researchers who work at the cusp of analysis and logic. The emphasis is on active research topics; many results are presented that have not been published before and open problems are formulated. Considerable effort has been made by the authors to integrate their articles and make them accessible to mathematicians new to the area.
    Note: Title from publisher's bibliographic system (viewed on 05 Oct 2015) , Ultraproducts in Analysis , Actions of Polish Groups and Classification Problems , On Subspaces, Asymptotic Structure, and Distortion of Banach Spaces; Connections with Logic
    Additional Edition: ISBN 9780521648615
    Additional Edition: ISBN 9780521648615
    Additional Edition: ISBN 9780521648615
    Additional Edition: Erscheint auch als Analysis and logic Cambridge [u.a.] : Cambridge University Press, 2002 ISBN 9780521648615
    Additional Edition: ISBN 0521648610
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 9780521648615
    Language: English
    Subjects: Mathematics
    RVK:
    SI 320
    Keywords: Analysis ; Mathematische Logik
    DOI: 10.1017/CBO9781107360006
    URL: Volltext
    URL: Inhaltstext
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    Online Resource
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    UB Potsdam
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