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)

@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},
 mrnumber = {2897749},
 mrclass = {03E35 (03E50)},
 doi = {10.1007/s12215-011-0078-7}
}