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
Autonomous Fixed Point Progressions and Fixed Point Transfinite Recursion
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. 449 - 464Publisher: Cambridge University PressPrint publication year: 2000
References
1. . On the relationship between ATR0 and ID. Journal of Symbolic Logic, 61(3):768–779, 1996.Google Scholar
2. . Admissible Sets and Structures: An Approach to Definability Theory. Springer, Berlin, 1975.
3. . A language and axioms for explicit mathematics. In , editor, Algebra and Logic, volume 450 of Lecture Notes in Mathematics, pages 87–139. Springer, Berlin, 1975.
4. Constructive theories of functions and classes. In , , and , editors, Logic Colloquium '78, pages 159–224. North Holland, Amsterdam, 1979.
5. . Iterated inductive fixed-point theories: application to Hancock's conjecture. In , editor, The Patras Symposion, pages 171–196. North Holland, Amsterdam, 1982.
6. , , and . A finite combinatorial principle which is equivalent to the 1-consistency of predicative analysis. In , editor, Patras Symposion, pages 197–230. North Holland, Amsterdam, 1982.
7. . Theories for iterated jumps, 1980. Handwritten notes.
8. . The strength of admissibility without foundation. The Journal of Symbolic Logic, 49 (3):867–879, 1984.Google Scholar
9. . Theories for Admissible Sets: A Unifying Approach to Proof Theory. Bibliopolis, Napoli, 1986.
10. , , , and . The proof-theoretic analysis of transfinitely iterated fixed point theories. Journal of Symbolic Logic. To appear.
11. and . Fixed point theories and dependent choice. Archive for Mathematical Logic. To appear.
12. and . Upper bounds for metapredicative Mahlo in explicit mathematics and admissible set theory. In preparation.
13. . Applicative Theories and Frege Structures. PhD thesis, Institut für Informatik und angewandte Mathematik, Universität Bern, 1997.
14. . Uniform limit in explicit mathematics with universes. Technical Report IAM-97-002, Institut für Informatik und angewandte Mathematik, Universität Bern, 1997.
15. . Intutionistic Type Theory, volume 1 of Studies in Proof Theory. Bibliopolis, 1984.
16. . Predicative Theories of Types and Names. PhD thesis, Institut f ür Informatik und angewandte Mathematik, Universität Bern, 1993.
17. . Universes in the theory of types and names. In et al., editor, Computer Science Logic '92, volume 702 of Lecture Notes in Computer Science, pages 340–351. Springer, Berlin, 1993.
18. and . The μ quantification operator in explicit mathematics with universes and iterated fixed point theories with ordinals.Archive for Mathematical Logic, 37(5+6):391–413, 1998.Google Scholar
19. . On universes in type theory. In and , editors, Twentyfive Years of Type Theory. Oxford University Press. To appear.
20. . Proof Theory: An Introduction, volume 1407 of Lecture Notes in Mathematics. Springer, Berlin, 1988.
21. . The strength of Martin-Löf type theory with a superuniverse. Part I.Archive for Mathematical Logic. To appear.
22. Proof-theoretic analysis of KPm. Archive for Mathematical Logic, 30:377–403., 1991.Google Scholar
23. . Kennzeichnung von Ordnungszahlen durch rekursiv erklärte Funktionen. Mathematische Annalen, 127:15–32, 1954.Google Scholar
24. . Proof Theory. Springer, Berlin, 1977.
25. . Σ1/1 and Σ1/1 transfinite induction. In , , and , editors, Logic Colloquium '80, pages 239–253. North Holland, Amsterdam, 1982.
26. . Subsystems of Second Order Arithmetic. Perspectives inMathematical Logic. Springer-Verlag, 1998.
27. . First steps into metapredicativity in explicit mathematics. In and , editors, Sets and Proofs. Cambridge University Press. To appear.
28. . Wellordering proofs for metapredicative Mahlo. In preparation.
- 3
- Cited by