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2006 Level Compactness
Gillman Payette, Blaine d'Entremont
Notre Dame J. Formal Logic 47(4): 545-555 (2006). DOI: 10.1305/ndjfl/1168352667


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.


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Gillman Payette. Blaine d'Entremont. "Level Compactness." Notre Dame J. Formal Logic 47 (4) 545 - 555, 2006.


Published: 2006
First available in Project Euclid: 9 January 2007

zbMATH: 1128.03016
MathSciNet: MR2272088
Digital Object Identifier: 10.1305/ndjfl/1168352667

Primary: 03B53
Secondary: 03B22 , 28B10

Keywords: compactness , Forcing , level , measure , paraconsistent logic

Rights: Copyright © 2006 University of Notre Dame


Vol.47 • No. 4 • 2006
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