Table of Contents

Part I: Proof Theoretic Analysis 1. Ordinal analysis without proofs 2. Relating ordinals to proofs in a perspicuous way 3. Internal finite tree embeddings 4. Foundational and mathematical uses of higher types 5. The epsilon substitution method and continuity 6. Predicativity: The outer limits Part II: Logic And Computation 7. A pragmatic interpretation of substructural logics 8. Computational complexity and induction for partial computable functions in type theory 9. Computability theory: Structure or algorithms 10. Tim Fernando 11. Three processes in natural language interpretation 12. Infinitary initial algebra specifications for stream algebras Part III: Applicative and Self-Applicative Theories 13. On extensionality, uniformity and comprehension in the theories of operations and classes 14. The proof-theoretic analysis of the Suslin operator in applicative theories 15. Feferman-Landin Logic 16. Explicit mathematics with monotone inductive definitions: A survey Part IV: Philosophy of Modern Mathematical and Logical Thought 17. On the constructivity of proofs. a debate among Behmann, Bernays, Godel, and Kaufmann 18. Realism and the debate on impredicativity, 1917–1944 19. Calculations by man and machine: Conceptual analysis 20. Remarks on finitism 21. Logical constants: The variable fortunes of an elusive notion

About the Author

Sieg , Wilfried; Sommer , Richard; Talcott , Carolyn

Reviews

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