Notre Dame Journal of Formal Logic

Level Compactness

Gillman Payette and Blaine d'Entremont

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.

Article information

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

Dates
First available in Project Euclid: 9 January 2007

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1168352667

Digital Object Identifier
doi:10.1305/ndjfl/1168352667

Mathematical Reviews number (MathSciNet)
MR2272088

Zentralblatt MATH identifier
1128.03016

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

Keywords
measure level paraconsistent logic compactness forcing

Citation

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


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References

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