Ultrafilter extensions of asymptotic density
نویسندگان
چکیده
منابع مشابه
Ultrafilter Extensions for Coalgebras
This paper studies finitary modal logics as specification languages for Set-coalgebras (coalgebras on the category of sets) using Stone duality. It is wellknown that Set-coalgebras are not semantically adequate for finitary modal logics in the sense that bisimilarity does not in general coincide with logical equivalence. Stone-coalgebras (coalgebras over the category of Stone spaces), on the ot...
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Proof: By assumption, φinf is preserved under ultrafilter extensions. The second conjunct of θ, i.e., ∀xy.(x = y → Rxy) is also preserved under ultrafilter extension, since it is modally definable using global modality. Finally, consider the third conjunct of θ. From the fact that M |= ∀xy.(x = y → Rxy), we can derive that the denotation of R in ueM includes all pairs of ultrafilters (u, v) suc...
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ژورنال
عنوان ژورنال: Commentationes Mathematicae Universitatis Carolinae
سال: 2019
ISSN: 0010-2628,1213-7243
DOI: 10.14712/1213-7243.2015.279