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.
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
Sieg \, Wilfried; Sommer \, Richard; Talcott \, Carolyn
Forms of assertion for a style of reasoning arise by fixing the meanings of some expressions . . . -Zentralblatt MATH, February 2005