UID:
almafu_9958100862302883
Umfang:
1 online resource (474 p.)
ISBN:
1-281-11996-2
,
9786611119966
,
0-08-053558-5
Serie:
Studies in logic and the foundations of mathematics ; v. 135
Inhalt:
This English translation of the author's original work has been thoroughly revised, expanded and updated. The book covers logical systems known as type-free or self-referential. These traditionally arise from any discussion on logical and semantical paradoxes. This particular volume, however, is not concerned with paradoxes but with the investigation of type-free sytems to show that: (i) there are rich theories of self-application, involving both operations and truth which can serve as foundations for property theory and formal semantics; (ii) these theories provide a new outlo
Anmerkung:
Description based upon print version of record.
,
Front Cover; Logical Frameworks for Truth and Abstraction: An Axiomatic Study; Copyright Page; Preface; Contents; Introduction; Part A: Combinators and Truth; Chapter I. Introducing operations; 1. The basic language; 2. Operations I: general facts; 3. Operations II: elementary recursion theory; 4A. The Church-Rosser theorem; 4B. Term models; 5. The graph model; 6. An effective version of the extensional model D; Appendix; Chapter II. Extending operations with reflective truth; 7. Extending combinatory algebras with truth; 8. The theory of operations and reflective truth: simple consequences
,
9A. Type-free abstraction, predicates and classes9B. Operations on predicates and classes; 10A. The fixed point theorem for predicates; 10B. Applications to semantScs and recursion theory; 11. Non-extensionality; Appendix I: a property theoretic definition of the fixed point operator for predicates; Appendix II: on the explicit abstraction theorem; Appendix III: independence of truth predicates from the encoding of logical operators; Part B: Truth and recursion Theory; Chapter III. Inductive models and definability theory; 12. Inductive models and the induction theorem
,
13. The envelope of an inductive model14. The uniform ordinal comparison theorem for inductive models; 15. Applications of the uniform ordinal comparison theorem; Chapter IV. Type-free abstraction with approximation operator; 16. Approximating properties by classes; 17. The approximation theorem for extensional operations and the fixed point theorem for monotone operations; 18. Topology displayed: basic definitions; 19. The representation theorem for explicitly CL-continuous operators; Appendix: alternative proofs; Chapter V. Type-free abstraction, choice and sets
,
20. Choice principles and the distinction between operations and functions21. Admissible hulls: elementary facts; 22. A model of admissible set theory; 23. The boundedness theorem; Part C: Selected Topics; Chapter VI. Levels of implication and intensional logical equivalence; 24. Myhill's levels of implication; 25. Formal deducibility based on levels of implication and its proof-theoretic strength; 26. Introducing an intensional equivalence relation; 27. The infinitary reduction relation; 28. The Church-Rosser theorem for; 29. A model of type-free logic based on intensional equivalence
,
Chapter VII. On the global structure of models for reflective truth30. The lattice of fixed point models for the neutral minimal theory; 31. The sublattice of intrinsic fixed point models and the cardinality theorem; 32. Variations on the encoding technique: non-modularity and other oddities; 33. A model for an impredicative extension of reflective truth; 34. On Kripke's classification of self-referential sentences; 35. On the consistency of coinduction principles; Appendix: a variant to the basic operator F and the restriction axiom; Part D: Levels of Truth and Proof Theory
,
Chapter VIII. Levels of reflective truth
,
English
Weitere Ausg.:
ISBN 0-444-82306-9
Sprache:
Englisch
Bookmarklink
