Generic Partial Two-Point Sets Are Extendable

1999 ◽  
Vol 42 (1) ◽  
pp. 46-51 ◽  
Author(s):  
Jan J. Dijkstra
Keyword(s):  
Point Sets ◽  
Martin's Axiom ◽  
Martin’S Axiom ◽  
Almost All

AbstractIt is shown that under ZFC almost all planar compacta that meet every line in at most two points are subsets of sets that meet every line in exactly two points. This result was previously obtained by the author jointly with K. Kunen and J. vanMill under the assumption that Martin’s Axiom is valid.

scholarly journals Construction of dual modules using Martin's Axiom

2008 ◽  
Vol 320 (6) ◽  
pp. 2388-2404
Author(s):  
Rüdiger Göbel ◽  
Sebastian Pokutta
Keyword(s):  
Martin's Axiom ◽  
Martin’S Axiom

scholarly journals Strongly Summable Ultrafilters, Union Ultrafilters, and the Trivial Sums Property

2016 ◽  
Vol 68 (1) ◽  
pp. 44-66 ◽  
Author(s):  
David J. Fernández Bretón
Keyword(s):  
Abelian Group ◽  
Partial Orders ◽  
Martin's Axiom ◽  
Martin’S Axiom ◽  
The Given

AbstractWe answer two questions of Hindman, Steprāns, and Strauss; namely, we prove that every strongly summable ultrafilter on an abelian group is sparse and has the trivial sums property. Moreover, we show that in most cases the sparseness of the given ultrafilter is a consequence of its being isomorphic to a union ultrafilter. However, this does not happen in all cases; we also construct (assuming Martin's Axiom for countable partial orders, i.e., , a strongly summable ultrafilter on the Boolean group that is not additively isomorphic to any union ultrafilter.

The equivalence of a generalized Martin's axiom to a combinatorial principle

1981 ◽  
Vol 46 (4) ◽  
pp. 817-821 ◽  
Author(s):  
William Weiss
Keyword(s):  
Combinatorial Principle ◽  
Martin's Axiom ◽  
Martin’S Axiom

AbstractA generalized version of Martin's axiom, called BACH, is shown to be equivalent to one of its combinatorial consequences, a generalization of P(c).

Countable dense homogeneous spaces under Martin’s axiom

1989 ◽  
Vol 65 (2) ◽  
pp. 153-164 ◽  
Author(s):  
Stewart Baldwin ◽  
Robert E. Beaudoin
Keyword(s):  
Homogeneous Spaces ◽  
Martin's Axiom ◽  
Martin’S Axiom
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