Logical Frameworks for Truth and Abstraction
An Axiomatic StudyBy
- A. Cantini, University of Florence, Department of Philosophy, Italy
Studies in Logic and the Foundations of Mathematics
Published: March 1996
...This is an appealing book, (relatively) easy to read, and attractive in its unified treatment of a range of issues...I found this to be a well-constructed book. The bibliography is thorough, and the indexes are well constructed and accurate...
E. Martin, Studia Logica
- Preface. Contents. Introduction. PART A: COMBINATORS AND TRUTH. I. Introducing operations. II. Extending operations with reflective truth. PART B: TRUTH AND RECURSION THEORY. III. Inductive models and definability theory. IV. Type-free abstraction with approximation operator. V. Type-free abstraction, choice and sets. PART C: SELECTED TOPICS. VI. Levels of implication and intentional logical equivalence. VII. On the global structure of models for reflective truth. PART D: LEVELS OF TRUTH AND PROOF THEORY. VIII. Levels of reflective truth. IX. Levels of truth and predicative well-orderings. X. Reducing reflective truth with levels to finitely iterated reflective truth. XI. Proof-theoretic investigation of finitely iterated reflective truth. PART E: ALTERNATIVE VIEWS. XII. Non-reductive systems for type-free abstraction and truth. XIII. The variety of non-reductive approaches. XIV. Epilogue: applications and perspectives. Bibliography. Index. List of Symbols.