Book contents
- Frontmatter
- Preface
- Opening speech of Petr Vopěnka
- Bolzano Medal awarded to Gaisi Takeuti
- Contents
- Collapsing Polynomial-Time Degrees
- Qualitative and Probabilistic Models of Full Belief
- Relative Splittings of in the-Enumeration Degrees
- A Realizability Interpretation for Classical Arithmetic
- An Axiomatization of Quantified Propositional Gödel Logic Using the Takeuti-Titani Rule
- Another Pathological Well-Ordering
- How Small Can the Set of Generics Be?
- Entailment Relations and Distributive Lattices
- The Friedberg Jump Inversion Theorem Revisited: A Study of Undefinable Cuts
- Hartley Rogers’ 1965 Agenda
- Liftings of Homomorphisms Between Quotient Structures and Ulam Stability
- Mathematical Fuzzy Logic – State of Art
- Reflections on the Last Delfino Problem
- Continuous Images of Coanalytic Sets
- Classification of Subsheaves over GL-Algebras
- On the Bit-Comprehension Rule
- Cardinal Invariants Associated with Predictors
- A Theorem on Countable Ordered Sets with an Application to Universal Graphs
- Dimension Theory and Smooth Stratification of Rigid Subanalytic Sets
- The Ramsey Structure of A-Determined Sets in a Saturated Universe
- On Definability of Admissible Sets
- Additive Theories
- Adding Multiplication to an O-minimal Expansion of the Additive Group of Real Numbers
- The Superjump in Martin-Löf Type Theory
- “Just Because”: Taking Belief Bases Seriously
- Artin Approximation via the Model Theory of Cohen-Macaulay Rings
- Ordinal Systems, Part 2: One Inaccessible
- Autonomous Fixed Point Progressions and Fixed Point Transfinite Recursion
- Finitary Reductions for Local Predicativity, I: Recursively Regular Ordinals
- The Complexity of Linear Logic with Weakening
- Some Remarks on the Maximality of Inner Models
- Author Index
- References
A Realizability Interpretation for Classical Arithmetic
Published online by Cambridge University Press: 31 March 2017
Book contents
- Frontmatter
- Preface
- Opening speech of Petr Vopěnka
- Bolzano Medal awarded to Gaisi Takeuti
- Contents
- Collapsing Polynomial-Time Degrees
- Qualitative and Probabilistic Models of Full Belief
- Relative Splittings of in the-Enumeration Degrees
- A Realizability Interpretation for Classical Arithmetic
- An Axiomatization of Quantified Propositional Gödel Logic Using the Takeuti-Titani Rule
- Another Pathological Well-Ordering
- How Small Can the Set of Generics Be?
- Entailment Relations and Distributive Lattices
- The Friedberg Jump Inversion Theorem Revisited: A Study of Undefinable Cuts
- Hartley Rogers’ 1965 Agenda
- Liftings of Homomorphisms Between Quotient Structures and Ulam Stability
- Mathematical Fuzzy Logic – State of Art
- Reflections on the Last Delfino Problem
- Continuous Images of Coanalytic Sets
- Classification of Subsheaves over GL-Algebras
- On the Bit-Comprehension Rule
- Cardinal Invariants Associated with Predictors
- A Theorem on Countable Ordered Sets with an Application to Universal Graphs
- Dimension Theory and Smooth Stratification of Rigid Subanalytic Sets
- The Ramsey Structure of A-Determined Sets in a Saturated Universe
- On Definability of Admissible Sets
- Additive Theories
- Adding Multiplication to an O-minimal Expansion of the Additive Group of Real Numbers
- The Superjump in Martin-Löf Type Theory
- “Just Because”: Taking Belief Bases Seriously
- Artin Approximation via the Model Theory of Cohen-Macaulay Rings
- Ordinal Systems, Part 2: One Inaccessible
- Autonomous Fixed Point Progressions and Fixed Point Transfinite Recursion
- Finitary Reductions for Local Predicativity, I: Recursively Regular Ordinals
- The Complexity of Linear Logic with Weakening
- Some Remarks on the Maximality of Inner Models
- Author Index
- References
- Type
- Chapter
- Information
- Logic Colloquium '98 , pp. 57 - 90Publisher: Cambridge University PressPrint publication year: 2000
References
1. Intepreting classical theories in constructive ones. Submitted.
2. and Gödel's functional (Dialectica) interpretation. In Buss [7].
3. , editor. The Handbook of Mathematical Logic. North-Holland, Amsterdam, 1977.
4. Notation systems for infinitary derivations. Archive for Mathematical Logic, 30:277–296, 1991.Google Scholar
5. Explaining the Gentzen-Takeuti reduction steps. Preliminary version, 1997.
6. The witness function method and provably recursive functions of Peano arithmetic. In , , editor, Proceedings of the Ninth International Congress on Logic, Methodology, and Philosophy of Science, Uppsala, Sweden, 1991, pages 29–68. Elsevier North-Holland, Amsterdam, 1994.
7. , editor. The Handbook of Proof Theory. North-Holland, To appear.
8. and Applications of a representation theory to subsystems of arithmetic. Preprint, 1998.
9. Classically and intuitionistically provable functions. In and , editors, Higher Set Theory, Lecture Notes in Mathematics 669, pages 21–27. Springer-Verlag, Berlin, 1978.
10. Untersuchungen über das logische Schliessen. Mathematische Zeitschrift, 39:176–210, 405–431, 1935. Translated as “Investigations into Logical Deduction” in [12], pages 68–131.
11. Neue Fassung des Widerspruchsfreiheit f ür die reineZahlentheorie. Forschungen zur Logik und zur Grundlegung der exakten Wissenschaften, New Series 4:19–44, 1938. Translated as “New Version of the Consistency Proof for Elementary Number Theory” in [12], pages 252–286.Google Scholar
12. Collected Works. North-Holland, Amsterdam, 1969. Edited by
13. über eine bisher noch nicht benü tzte Erweiterung des finiten Standpunktes. Dialectica, 12:280–287, 1958. Reproduced with English translation in [14], pp. 241–251.Google Scholar
14. Collected Works, volume II. Oxford University Press, New York, 1990. et al. eds.
15. and Introduction to Combinators and Σ-calculus. Cambridge University Press, Cambridge, 1986.
16. Normalization of finite terms and derivations via infinite ones. [18], pages 73–76.
17. Grigorii E.Mints. On E-theorems. [18], pages 105–115.
18. Selected Papers in Proof Theory. Bibliopolis / North-Holland, Naples / Amsterdam, 1992.
19. An evaluation semantics for classical proofs. In Proceedings, SixthAnnual IEEE Symposium on Logic in Computer Science, pages 96–107, Amsterdam, 1991.
20. On the consistency of classical formal arithmetic. Russian Acad.Sci. Dokl. Math., 48, 1994. See alsoMathematical Reviews, 98j:03081.Google Scholar
21. Proofs of strong normalization for second order classical natural deduction. Journal of Symbolic Logic, 62(4):1461–1479, 1997.Google Scholar
23. . Natural Deduction: A Proof-theoretical Study. Almquist and Wiksell, Stockholm, 1965.
22. Proof Theory: An Introduction. Lecture Notes in Mathematics #1407. Springer-Verlag, Berlin, 1989.
24. Proof theory: Some aspects of cut-elimination. In Barwise [3], pages 867–895.
25. Proof Theory. North-Holland, Amsterdam, second edition, 1987.
26. Introductory note to 1958 and 1972. In [14], pages 217–241.
27. Aspects of constructive mathematics. In Barwise [3], pages 973–1052.
28. Realizability. In Buss [7].
29. Logic and Structure. Springer, Berlin, third edition, 1997.
30. The correspondence between cut-elimination and normalization I, II. Annals of Mathematical Logic, 7:1–156, 1974.Google Scholar