Level Compactness
Notre Dame Journal of Formal Logic 47 (4):545-555 (2006)
| Abstract | The concept of compactness is a necessary condition of any system that is going to call itself a finitary method of proof. However, it can also apply to predicates of sets of formulas in general and in that manner it can be used in relation to level functions, a flavor of measure functions. In what follows we will tie these concepts of measure and compactness together and expand some concepts which appear in d'Entremont's master's thesis, "Inference and Level." We will also provide some applications of the concept of level to the "preservationist" program of paraconsistent logic. We apply the finite level compactness theorem in this paper to get a Lindenbaum flavor extension lemma and a maximal "forcibility" theorem. Each of these is based on an abstract deductive system X which satisfies minimal conditions of inference and has generalizations of 'and' and 'not' as logical words. | |||||||||
| 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: 5,701 |
| External links |
  Try with proxy. |
| Through your library | Configure |
Similar books and articlesArthur W. Apter & Joel David Hamkins (2002). Indestructibility and the Level-by-Level Agreement Between Strong Compactness and Supercompactness. Journal of Symbolic Logic 67 (2):820-840.
Alexander Paseau (2011). Proofs of the Compactness Theorem. History and Philosophy of Logic 31 (1):73-98.
Mark Howard (1988). A Proofless Proof of the Barwise Compactness Theorem. Journal of Symbolic Logic 53 (2):597-602.
Ehud Hrushovski & Itamar Pitowsky (2004). Generalizations of Kochen and Specker's Theorem and the Effectiveness of Gleason's Theorem. Studies in History and Philosophy of Science Part B 35 (2):177-194.
Samir Chopra & Eric Martin (2002). Generalized Logical Consequence: Making Room for Induction in the Logic of Science. Journal of Philosophical Logic 31 (3):245-280.
Itamar Pitowsky (2004). Generalizations of Kochen and Specker's Theorem and the Effectiveness of Gleason's Theorem. Studies in History and Philosophy of Science Part B 35 (2):177-194.
Michael Scanlan (1983). On Finding Compactness in Aristotle. History and Philosophy of Logic 4 (1&2):1-8.
Petr Cintula (2005). Two Notions of Compactness in Gödel Logics. Studia Logica 81 (1):99 - 122.
John W. Dawson (1993). The Compactness of First-Order Logic:From Gödel to Lindström. History and Philosophy of Logic 14 (1):15-37.
Steffen Lewitzka & Andreas B. M. Brunner (2009). Minimally Generated Abstract Logics. Logica Universalis 3 (2).
Arthur W. Apter (1981). Measurability and Degrees of Strong Compactness. Journal of Symbolic Logic 46 (2):249-254.
Attila R. Imre (2006). Compactness Versus Interior-to-Edge Ratio; Two Approaches for Habitat's Ranking. Acta Biotheoretica 54 (1).
Daniele Mundici (1986). Inverse Topological Systems and Compactness in Abstract Model Theory. Journal of Symbolic Logic 51 (3):785-794.
John M. Vickers (1990). Compactness in Finite Probabilistic Inference. Journal of Philosophical Logic 19 (3):305 - 316.
Christopher Menzel (1989). On an Unsound Proof of the Existence of Possible Worlds. Notre Dame Journal of Formal Logic 30 (4):598-603.
Analytics
Monthly downloads |
Added to index2010-08-24Total downloads7 ( #133,532 of 549,108 )Recent downloads (6 months)1 ( #63,361 of 549,108 )How can I increase my downloads? |
My notes
Discussion
