David Fernandez: Two microcontributions to the theory of Strongly Summable Ultrafilters

4 April 2014, 13:30–15:00

Fields institute, Room 210

Speaker:  David Fernandez

Title:  Two microcontributions to the theory of Strongly Summable Ultrafilters

Strongly Summable Ultrafilters are those generated by FS-sets (where FS(X) is the set of all possible sums of finitely many elements from X (you can only add each element once)). I will show two little results (with nice little neat proofs!) about these: first, that every strongly summable ultrafilter on the countable Boolean group is rapid. Second, that there is a model where strongly summable ultrafilters (on any abelian group really, but without loss of generality on the countable Boolean group) exist yet Martin’s axiom for countable forcing notions fails (up until now, these ultrafilters were only known to exist under this hypothesis).

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