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Reflections on the Foundations of Mathematics

Reflections on the Foundations of Mathematics
Essays in Honor of Solomon Feferman

$111.00 ( ) USD

Part of Lecture Notes in Logic

Jeremy Avigad, Wilfried Buchholz, Harvey M. Friedman, Ulrich Kohlenbach, Grigori Mints, Stephen G. Simpson, Gianluigi Bellin, Carlo Dalla Pozza, Robert L. Constable, Karl Crary, Jens Erik Fenstad, Tim Fernando, J. V. Tucker, J. I. Zucker, Andrea Cantini, Gerhard Jäger, Thomas Strahm, Ian A. Mason, Carolyn L. Talcott, Michael Rathjen, Paolo Mancosu, Charles Parsons, Wilfried Sieg, W. W. Tait, Johan van Benthem
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  • Publication planned for: April 2020
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9781316998816

$ 111.00 USD ( )
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About the Authors
  • 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. This volume, the fifteenth publication in the Lecture Notes in Logic series, collects papers presented at the symposium 'Reflections on the Foundations of Mathematics' held in celebration of Solomon Feferman's 70th birthday (The 'Feferfest') at Stanford University, California in 1988. Feferman has shaped the field of foundational research for nearly half a century. These papers reflect his broad interests as well as his approach to foundational research, which emphasizes the solution of mathematical and philosophical problems. There are four sections, covering proof theoretic analysis, logic and computation, applicative and self-applicative theories, and philosophy of modern mathematical and logic thought.

    • A collection of twenty papers from leading logicians
    • Reflects Solomon Feferman's broad range of interests and his approach to foundational work
    • Of interest to all researchers and students in mathematical logic
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    Product details

    • Publication planned for: April 2020
    • format: Adobe eBook Reader
    • isbn: 9781316998816
    • contains: 14 b/w illus.
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    Preface
    Part I. Proof Theoretic Analysis:
    1. Ordinal analysis without proofs Jeremy Avigad
    2. Relating ordinals to proofs in a perspicuous way Wilfried Buchholz
    3. Internal finite tree embeddings Harvey M. Friedman
    4. Foundational and mathematical uses of higher types Ulrich Kohlenbach
    5. The epsilon substitution method and continuity Grigori Mint
    6. Predicativity: the outer limits Stephen G. Simpson
    Part II. Logic and Computation:
    7. A pragmatic interpretation of substructural logics Gianluigi Bellin and Carlo Dalla Pozza
    8. Computational complexity and induction for computable functions in type theory Robert L. Constable and Karl Crary
    9. Computability theory: structure or algorithms Jens Erik Fenstad
    10. Three processes in natural language interpretation Tim Fernando
    11. Infinitary initial algebra specifications for stream algebras J. V. Tucker and J. I. Zucker
    Part III. Applicative and Self-Applicative Theories:
    12. On extensionality, uniformity and comprehension in the theories of operations and classes Andrea Cantini
    13. The proof-theoretic analysis of the Suslin operator in applicative theories Gerhard Jäger and Thomas Strahm
    14. Feferman-Landin logic Ian A. Mason and Carolyn L. Talcott
    15. Explicit mathematics with monotone inductive definitions: a survey Michael Rathjen
    Part IV. Philosophy of Modern Mathematical and Logical Thought:
    16. On the constructivity of proofs: a debate among Behmann, Bernays, Gödel, and Kaufmann Paolo Mancosu
    17. Realism and the debate on impredicativity, 1917–44 Charles Parsons
    18. Calculations by man and machine: conceptual analysis Wilfried Sieg
    19. Remarks on finitism W. W. Tait
    20. Logical constraints: the variable fortunes of an elusive notion Johan van Benthem
    Symposium program.

  • Editors

    Wilfried Sieg, Carnegie Mellon University, Pennsylvania
    Wilfrid Sieg works in the Department of Philosophy at Carnegie Mellon University, Pennsylvania.

    Richard Sommer, Stanford University, California
    Richard Sommer works in the Center for the Study of Language and Information at Stanford University, California.

    Carolyn Talcott, Stanford University, California
    Carolyn Talcott works in the Computer Science Department at Stanford University, California.

    Contributors

    Jeremy Avigad, Wilfried Buchholz, Harvey M. Friedman, Ulrich Kohlenbach, Grigori Mints, Stephen G. Simpson, Gianluigi Bellin, Carlo Dalla Pozza, Robert L. Constable, Karl Crary, Jens Erik Fenstad, Tim Fernando, J. V. Tucker, J. I. Zucker, Andrea Cantini, Gerhard Jäger, Thomas Strahm, Ian A. Mason, Carolyn L. Talcott, Michael Rathjen, Paolo Mancosu, Charles Parsons, Wilfried Sieg, W. W. Tait, Johan van Benthem

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