Ultrafilters (with Dense Elements) over Closure Spaces

Roland Hinnion

Ultrafilters (with Dense Elements) over Closure Spaces

Publication date: 23.08.2012

Reports on Mathematical Logic, 2012, Number 47, pp. 115-124

https://doi.org/10.4467/20842589RM.12.005.0686

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Ultrafilters (with Dense Elements) over Closure Spaces

Abstract

Several notions and results that are useful for directed sets (and their applications) can be extended to the more general context of closure spaces; inter alia the so-called "ﬁnite intersection property" and the existence of special ultraﬁlters (namely ultraﬁlters which elements are dense) on such structures.

Keywords

closure space, density, ultraﬁlter, ﬁnite intersection property

References

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[1] C.C. Chang and H.J. Keisler, Model Theory, North-Holland 1973.

[2] O. Esser and R. Hinnion, Large cardinals and ramiﬁability for directed sets, Mathematical Logic Quarterly 46 (2000), pp. 25–34.

[3] O. Esser and R. Hinnion, Combinatorial criteria for ramiﬁable ordered sets, Mathematical Logic Quarterly 47 (2001), pp. 539–555.

[4] O. Esser and R. Hinnion, Tree-properties for ordered sets, Mathematical Logic Quarterly 48 (2002), pp. 213–219.

[5] R. Hinnion, Directed sets and Malitz-Cauchy completions, Mathematical Logic Quarterly 43 (1997), pp. 465–484.

[6] R. Hinnion, Ramiﬁable directed sets, Mathematical Logic Quarterly 44 (1998), pp. 216–228.

[7] R. Hinnion, A general Cauchy-completion process, Logique & Analyse 197 (2007), pp. 5–41.

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Information: Reports on Mathematical Logic, 2012, Number 47, pp. 115-124

DOI: https://doi.org/10.4467/20842589RM.12.005.0686

Article type: Original article

Authors

Roland Hinnion

Université Libre de Bruxelles,

Published at: 23.08.2012

Article status: Open

Licence: None

Percentage share of authors:

Roland Hinnion (Author) - 100%

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English

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