Invariance properties of almost disjoint families
M Arciga-Alejandre, M Hrušák… - The Journal of …, 2013 - cambridge.org
M Arciga-Alejandre, M Hrušák, C Martinez-Ranero
The Journal of Symbolic Logic, 2013•cambridge.org… We consider two kinds of closely related mathematical structures in this paper: almost
disjoint families and cofinitary groups. An infinite family A ⊆ P( ) is almost disjoint (AD) if the
intersection of any two distinct elements of A is finite. It is maximal almost disjoint (MAD) if it
is not properly included in any larger AD family or, equivalently, if given an infinite set X ⊆ …
disjoint families and cofinitary groups. An infinite family A ⊆ P( ) is almost disjoint (AD) if the
intersection of any two distinct elements of A is finite. It is maximal almost disjoint (MAD) if it
is not properly included in any larger AD family or, equivalently, if given an infinite set X ⊆ …
We answer a question of Garcia-Ferreira and Hrušák by consistently constructing a MAD family maximal in the Katětov order. We also answer several questions of Garcia-Ferreira.
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