On absolutely Baire nonmeasurable functions

2019 ◽  
Vol 26 (4) ◽  
pp. 483-487
Author(s):  
Piotr Zakrzewski
Keyword(s):  
Baire Category ◽  
Additive Functions ◽  
Theoretic Result ◽  
Martin's Axiom ◽  
Martin’S Axiom

Abstract We shall show that under Martin’s axiom, there exist absolutely Baire nonmeasurable additive functions. This provides a Baire category counterpart of an analogous measure-theoretic result of A. B. Kharazishvili.

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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