Overview

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 outlook on classical topics, such as inductive definitions and predicative mathematics; (iii) they are particularly promising with regard to applications. Research arising from paradoxes has moved progressively closer to the mainstream of mathematical logic and has become much more prominent in the last twenty years. A number of significant developments, techniques and results have been discovered. Academics, students and researchers will find that the book contains a thorough overview of all relevant research in this field.

Full Product Details

Author:   A. Cantini (University of Florence, Department of Philosophy, Italy)
Publisher:   Elsevier Science & Technology
Imprint:   North-Holland
Volume:   v. 135
Dimensions:   Width: 15.60cm , Height: 2.70cm , Length: 23.40cm
Weight:   0.900kg
ISBN:  

9780444823069

ISBN 10:   0444823069
Pages:   460
Publication Date:   14 March 1996
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Out of Print
Availability:   In Print  
Limited stock is available. It will be ordered for you and shipped pending supplier's limited stock.

Table of Contents

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

Reviews

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... --Studia Logica

E. Martin ...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... Studia Logica

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