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Logical frameworks for truth and abstraction : an axiomatic study

Author: Andrea Cantini
Publisher: Amsterdam ; New York : Elsevier Science B.V., 1996.
Series: Studies in logic and the foundations of mathematics, v. 135.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This English translation of the author's original work has been thoroughly revised, expanded and updated. The book covers logical systems known as <IT>type-free</IT> or <IT>self-referential</IT>. 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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Cantini, Andrea.
Logical frameworks for truth and abstraction.
Amsterdam ; New York : Elsevier Science B.V., 1996
(DLC) 96004681
(OCoLC)34114796
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Andrea Cantini
ISBN: 9780444823069 0444823069 9780080535586 0080535585
OCLC Number: 162130519
Description: 1 online resource (xii, 461 pages) : illustrations.
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
Series Title: Studies in logic and the foundations of mathematics, v. 135.
Responsibility: Andrea Cantini.
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Abstract:

Covers logical systems known as type-free or self-referential. This book shows that there are theories of self-application, involving both operations and truth which can serve as foundations for  Read more...

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"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 Read more...

 
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