Reflections on the Foundations of Mathematics: Essays in Honor of Solomon Feferman: Lecture Notes in Logic 15

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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 his agenda. The contributions range from historical to technical to philosophical topics, with emphasis on proof theory and computational aspects.

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Forms of assertion for a style of reasoning arise by fixing the meanings of some expressions . . . -Zentralblatt MATH, February 2005
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Table of Contents

Ordinal analysis without proofs 1
Relating ordinals to proofs in a perspicuous way 37
Internal finite tree embeddings 60
Foundational and mathematical uses of higher types 92
The epsilon substitution method and continuity 117
Predicativity: The outer limits 130
A pragmatic interpretation of substructural logics 139
Computational complexity and induction for partial computable functions in type theory 164
Computability theory: structure or algorithms 182
Three processes in natural language interpretation 208
Infinitary initial algebra specifications for stream algebras 228
On extensionality, uniformity and comprehension in the theories of operations and classes 251
The proof-theoretic analysis of the Suslin operator in applicative theories 270
Feferman-Landin Logic 293
Explicit mathematics with monotone inductive definitions: A survey 329
On the constructivity of proofs. A debate among Behmann, Bernays, Godel, and Kaufmann 349
Realism and the debate on impredicativity. 1917-1944 372
Calculations by man and machine: conceptual analysis 390
Remarks on finitism 410
Logical constants: the variable fortunes of an elusive notion 420
Symposium program 443
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