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Completeness and interpolation of almost‐everywhere quantification over finitely additive measures
Author(s) -
Rasga João,
Lotfallah Wafik Boulos,
Sernadas Cristina
Publication year - 2013
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201110051
Subject(s) - mathematics , quantifier (linguistics) , completeness (order theory) , countable set , quantifier elimination , almost everywhere , consistency (knowledge bases) , discrete mathematics , property (philosophy) , interpolation (computer graphics) , gödel's completeness theorem , finitely generated abelian group , pure mathematics , computer science , artificial intelligence , mathematical analysis , philosophy , epistemology , motion (physics)
We give an axiomatization of first‐order logic enriched with the almost‐everywhere quantifier over finitely additive measures. Using an adapted version of the consistency property adequate for dealing with this generalized quantifier, we show that such a logic is both strongly complete and enjoys Craig interpolation, relying on a (countable) model existence theorem. We also discuss possible extensions of these results to the almost‐everywhere quantifier over countably additive measures.