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Self-reference and modal logic

Author: C Smoryński
Publisher: New York : Springer-Verlag, ©1985.
Series: Universitext.
Edition/Format:   Print book : EnglishView all editions and formats
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Additional Physical Format: Online version:
Smoryński, C.
Self-reference and modal logic.
New York : Springer-Verlag, ©1985
(OCoLC)1085904743
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: C Smoryński
ISBN: 0387962093 9780387962092 3540962093 9783540962090
OCLC Number: 12313885
Description: xii, 333 pages ; 24 cm.
Contents: 0. Introduction.- 1. The Incompleteness Theorems.- 2. Self-Reference.- 3. Things to Come.- 4. The Theory PRA.- 5. Encoding Syntax in PRA.- 6. Additional Arithmetic Prerequisites.- I. The Logic of Provability.- 1. Provability as Modality.- 1. A System of Basic Modal Logic.- 2. Provability Logic(s).- 3. Self-Reference in PRL.- 4. Avoiding R2.- 2. Modal Model Theory.- 1. Model Theory for BML.- 2. Model Theory for PRL.- 3. Models and Self-Reference.- 4. Another Provability Logic.- 3. Arithmetic Interpretations of PRL.- 1. Solovay's First Completeness Theorem.- 2. Solovay's Second Completeness Theorem.- 3. Generalisations, Refinements, and Analogues.- II. Multi-Modal Logic and Self-Reference.- 4. Bi-Modal Logics and Their Arithmetic Interpretations.- 1. Bi-Modal Self-Reference.- 2. Kripke Models.- 3. Carlson Models.- 4. Carlson's Arithmetic Completeness Theorem.- 5. Fixed Point Algebras.- 1. Boolean and Diagonalisable Algebras.- 2. Fixed Point Algebras.- 3. Discussion.- III. Non-Extensional Self-Reference.- 6. Rosser Sentences.- 1. Modal Systems for Rosser Sentences.- 2. Arithmetic Interpretations.- 3. Inequivalent Rosser Sentences.- 7. An Ubiquitous Fixed Point Calculation.- 1. An Ubiquitous Fixed Point Calculation.- 2. Applications.- 3. Relativisation to a Partial Truth Definition.- 4. Svejdar's Self-Referential Formulae.
Series Title: Universitext.
Responsibility: C. Smoryński.

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