Self-Reference and Modal Logic
It is Sunday, the 7th of September 1930. The place is Konigsberg and the occasion is a small conference on the foundations of mathematics. Arend Heyting, the foremost disciple of L. E. J. Brouwer, has spoken on intuitionism; Rudolf Carnap of the Vienna Circle has expounded on logicism; Johann (forme...
| Main Author: | |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1985, 1985
|
| Edition: | 1st ed. 1985 |
| Series: | Universitext
|
| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of 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
- 2. Modal Model Theory
- 3. Arithmetic Interpretations of PRL
- II. Multi-Modal Logic and Self-Reference
- 4. Bi-Modal Logics and Their Arithmetic Interpretations
- 5. Fixed Point Algebras
- III. Non-Extensional Self-Reference
- 6. Rosser Sentences
- 7. An Ubiquitous Fixed Point Calculation