Some unifying fixed point principles
Studia Logica 50 (1):129 - 141 (1991)
| Abstract | This article is written for both the general mathematican and the specialist in mathematical logic. No prior knowledge of metamathematics, recursion theory or combinatory logic is presupposed, although this paper deals with quite general abstractions of standard results in those three areas. Our purpose is to show how some apparently diverse results in these areas can be derived from a common construction. In Section 1 we consider five classical fixed point arguments (or rather, generalizations of them) which we present as problems that the reader might enjoy trying to solve. Solutions are given at the end of the section. In Section 2 we show how all these solutions can be obtained as special cases of a single fixed point theorem. In Section 3 we consider another generalization of the five fixed point results of Section 1 and show that this is of the same strength as that of Section 2. In Section 4 we show some curious strengthenings of results of Section 3 which we believe to be of some interest on their own accounts. | |||||||||
| Keywords | No keywords specified (fix it) | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,679 |
| External links |
 |
| Through your library | Configure |
Similar books and articlesKarl-Georg Niebergall (1999). Nonmonotonicity in (the Metamathematics of) Arithmetic. Erkenntnis 50 (2-3):309-332.
Philip Kremer (2009). Comparing Fixed-Point and Revision Theories of Truth. Journal of Philosophical Logic 38 (4):363 - 403.
Gregory McColm (2004). Guarded Quantification in Least Fixed Point Logic. Journal of Logic, Language and Information 13 (1):61-110.
Michael Rathjen (1999). Explicit Mathematics with the Monotone Fixed Point Principle. II: Models. Journal of Symbolic Logic 64 (2):517-550.
Anuj Dawar & Yuri Gurevich (2002). Fixed Point Logics. Bulletin of Symbolic Logic 8 (1):65-88.
Max Kubierschky (2000). Yet Another Hierarchy Theorem. Journal of Symbolic Logic 65 (2):627-640.
Raymond M. Smullyan (1994). Diagonalization and Self-Reference. Clarendon Press.
Philip Kremer (2008). Supervaluation Fixed-Point Logics of Truth. Journal of Philosophical Logic 37 (5).
Per Lindström (2006). Note on Some Fixed Point Constructions in Provability Logic. Journal of Philosophical Logic 35 (3):225 - 230.
Analytics
Monthly downloads |
Added to index2009-01-28Total downloads22 ( #56,207 of 549,087 )Recent downloads (6 months)0How can I increase my downloads? |
My notes
Discussion
