Notre Dame Journal of Formal Logic

Level Compactness

Gillman Payette and Blaine d'Entremont


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.

Article information

Notre Dame J. Formal Logic, Volume 47, Number 4 (2006), 545-555.

First available in Project Euclid: 9 January 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03B53: Paraconsistent logics
Secondary: 03B22: Abstract deductive systems 28B10: Group- or semigroup-valued set functions, measures and integrals

measure level paraconsistent logic compactness forcing


Payette, Gillman; d'Entremont, Blaine. Level Compactness. Notre Dame J. Formal Logic 47 (2006), no. 4, 545--555. doi:10.1305/ndjfl/1168352667.

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