scholarly journals A notion of selective ultrafilter corresponding to topological Ramsey spaces

2007 ◽  
Vol 53 (3) ◽  
pp. 255-267 ◽  
Author(s):  
José G. Mijares
Keyword(s):  
Selective Ultrafilter

THE NEXT BEST THING TO A P-POINT

2015 ◽  
Vol 80 (3) ◽  
pp. 866-900 ◽  
Author(s):  
ANDREAS BLASS ◽  
NATASHA DOBRINEN ◽  
DILIP RAGHAVAN
Keyword(s):  
Isomorphism Class ◽  
Partition Relations ◽  
Image Position ◽  
Selective Ultrafilter

AbstractWe study ultrafilters on ω2 produced by forcing with the quotient of ${\cal P}$(ω2) by the Fubini square of the Fréchet filter on ω. We show that such an ultrafilter is a weak P-point but not a P-point and that the only nonprincipal ultrafilters strictly below it in the Rudin–Keisler order are a single isomorphism class of selective ultrafilters. We further show that it enjoys the strongest square-bracket partition relations that are possible for a non-P-point. We show that it is not basically generated but that it shares with basically generated ultrafilters the property of not being at the top of the Tukey ordering. In fact, it is not Tukey-above [ω1]<ω, and it has only continuum many ultrafilters Tukey-below it. A tool in our proofs is the analysis of similar (but not the same) properties for ultrafilters obtained as the sum, over a selective ultrafilter, of nonisomorphic selective ultrafilters.

scholarly journals Countably compact groups from a selective ultrafilter

2004 ◽  
Vol 133 (3) ◽  
pp. 937-943 ◽  
Author(s):  
S. Garcia-Ferreira ◽  
A. H. Tomita ◽  
S. Watson
Keyword(s):  
Compact Groups ◽  
Countably Compact ◽  
Selective Ultrafilter
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