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Reflections on the foundations of mathematics : essays in honor of Solomon Feferman / edited by Wilfried Sieg, Richard Sommer, Carolyn Talcott.
Math/Physics/Astronomy Library QA9.A1 R44 2002
Available
- Format:
- Book
- Series:
- Lecture notes in logic ; 15.
- Lecture notes in logic ; 15
- Language:
- English
- Subjects (All):
- Logic, Symbolic and mathematical--Congresses.
- Logic, Symbolic and mathematical.
- Mathematics--Philosophy--Congresses.
- Mathematics.
- Mathematics--Philosophy.
- Genre:
- Conference papers and proceedings.
- Physical Description:
- xviii, 444 pages : illustrations ; 24 cm.
- Place of Publication:
- Natick, Mass. : AK Peters, 2002.
- Summary:
- Solomon Feferman has shaped the field of foundational research for nearly half a century. These papers, most of which were presented at the symposium honoring him at his 70th birthday, reflect his broad interests as well as his approach to foundational research, which places the solution of mathematical and philosophical problems at the top of the agenda. The contributions range from historical to technical to philosophical topics, with emphasis on proof theory and computational aspects.
- Contents:
- Part I Proof Theoretic Analysis
- Ordinal analysis without proofs / Jeremy Avigad 1
- Relating ordinals to proofs in a perspicuous way / Wilfried Buchholz 37
- Internal finite tree embeddings / Harvey M. Friedman 60
- Foundational and mathematical uses of higher types / Ulrich Kohlenbach 92
- The epsilon substitution method and continuity / Grigori Mints 117
- Predicativity: The outer limits / Stephen G. Simpson 130
- Part II Logic and Computation
- A pragmatic interpretation of substructural logics / Gianluigi Bellin, Carlo Dalla Pozza 139
- Computational complexity and induction for partial computable functions in type theory / Robert L. Constable, Karl Crary 164
- Computability theory: structure or algorithms / Jens Erik Fenstad 182
- Three processes in natural language interpretation / Tim Fernando 208
- Infinitary initial algebra specifications for stream algebras / J. V. Tucker, J. I. Zucker 228
- Part III Applicative and Self-Applicative Theories
- On extensionality, uniformity and comprehension in the theories of operations and classes / Andrea Cantini 251
- The proof-theoretic analysis of the Suslin operator in applicative theories / Gerhard Jager, Thomas Strahm 270
- Feferman-Landin Logic / Ian A. Mason, Carolyn L. Talcott 293
- Explicit mathematics with monotone inductive definitions: A survey / Michael Rathjen 329
- Part IV Philosophy of Modern Mathematical and Logical Thought
- On the constructivity of proofs. A debate among Behmann, Bernays, Godel, and Kaufmann / Paolo Mancosu 349
- Realism and the debate on impredicativity, 1917-1944 / Charles Parsons 372
- Calculations by man and machine: conceptual analysis / Wilfried Sieg 390
- Remarks on finitism / W. W. Tait 410
- Logical constants: the variable fortunes of an elusive notion / Johan van Benthem 420.
- Notes:
- Includes bibliographical references.
- ISBN:
- 1568811705
- OCLC:
- 49531184
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