Geodesic
MAD families, P + (I)-ideals and ideal convergence
Filomat, Tome 34 (2020) no. 9, p. 3099

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DOI

Let I be an ideal on ω, the notion of I-AD family was introduced in [3]. Analogous to the well studied ideal I(A) generated by almost disjoint families, we introduce and investigate the ideal I(I-A). It turns out that some properties of I(I-A) depends on the structure of I. Denoting by a(I) the minimum of the cardinalities of infinite I-MAD families, several characterizations for a(I) ≥ ω 1 will be presented. Motivated by the work in [23], we introduce the cardinality s ω,ω (I), and obtain a necessary condition for s ω,ω (I) = s(I). As an application, we show finally that if a(I) ≥ s(I), then BW property coincides with Helly property.
DOI : 10.2298/FIL2009099Y
Classification : 05D10, 40A35, 54A20
Keywords: MAD families, cardinality, Bolzano-Weierstrass property, Helly property, P+(I)-ideals 
Jiakui Yu; Shuguo Zhang. MAD families, P + (I)-ideals and ideal convergence. Filomat, Tome 34 (2020) no. 9, p. 3099 . doi: 10.2298/FIL2009099Y
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     author = {Jiakui Yu and Shuguo Zhang},
     title = {MAD families, {P} + {(I)-ideals} and ideal convergence},
     journal = {Filomat},
     pages = {3099 },
     year = {2020},
     volume = {34},
     number = {9},
     doi = {10.2298/FIL2009099Y},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2009099Y/}
}
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