C. Smoryński. Self-reference and modal logic. Universitext. Springer-Verlag, New York, Berlin, etc., 1985, xii + 333 pp.
George Boolos · Journal of Symbolic Logic · 1988
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.