# Sh:985

- Dow, A. S., & Shelah, S. (2012).
*Martin’s axiom and separated mad families*. Rend. Circ. Mat. Palermo (2),**61**(1), 107–115. DOI: 10.1007/s12215-011-0078-7 MR: 2897749 -
Abstract:

Two families \mathcal A, \mathcal B of subsets of \omega are said to be separated if there is a subset of \omega which mod finite contains every member of \mathcal A and is almost disjoint from every member of \mathcal B. If \mathcal A and \mathcal B are countable disjoint subsets of an almost disjoint family, then they are separated. Luzin gaps are well-known examples of of \omega_1-sized subfamilies of an almost disjoint family which can not be separated. An almost disjoint family will be said to be \omega_1-separated if any disjoint pair of {\leq}\omega_1-sized subsets are separated. It is known that the proper forcing axiom (PFA) implies that no maximal almost disjoint family is {\leq}\omega_1-separated. We prove that this does not follow from Martin’s Axiom. - published version (9p)

Bib entry

@article{Sh:985, author = {Dow, Alan Stewart and Shelah, Saharon}, title = {{Martin's axiom and separated mad families}}, journal = {Rend. Circ. Mat. Palermo (2)}, fjournal = {Rendiconti del Circolo Matematico di Palermo. Second Series}, volume = {61}, number = {1}, year = {2012}, pages = {107--115}, issn = {0009-725X}, doi = {10.1007/s12215-011-0078-7}, mrclass = {03E35 (03E50)}, mrnumber = {2897749}, doi = {10.1007/s12215-011-0078-7} }