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On certain I-ultrafilters and ip rich sets

FLAŠKOVÁ, J. On certain I-ultrafilters and ip rich sets. Mathematical Research and Conference Center, Bedlewo, 2009.
Jazyk publikace: eng
Anglický název: On certain I-ultrafilters and ip rich sets
Rok vydání: 2009
Autoři: RNDr. Jana Flašková Ph.D.
Abstrakt EN: We study special classes of ultrafilters on natural numbers and we focus on I-ultrafilters which were introduced by Baumgartner. We are particularly interested in the situation where I is an ideal on natural numbers. Summable ideals and the Hindman ideal are considered and the relations between the corresponding classes of ultrafilters are investigated. We show that there is no inclusion between the two classes of ultrafilters and that selective ultrafilters belong to both of them. Further, we consider also the ideal generated by sets which are not ip rich and describe how the class of corresponding I-ultrafilters is related to the previous ones and to P-points. Assuming Martin's axiom for countable posets we can construct several ultrafilters with various combinations of (not) being an I-ultrafilter and/or (not) being a J-ultrafilter where both I and J is either a summable ideal or Hindman ideal or ideal of not ip rich sets.
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