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Logic Seminar

Tuesday, March 27, 2018
1:00pm to 2:00pm
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Building 15, Room 131
Un-definability of mad families relative to a class of Borel ideals
Asger Törnquist, Department of Mathematical Sciences, University of Copenhagen,
Many are familiar with the classic result due to Mathias that there are no analytic infinite maximal almost disjoint families, where almost disjoint means "having finite intersection". In this talk I will discuss what happens if we replace "having finite intersection" with "having intersection in a (fixed) ideal I", where I is a Borel ideal on $\omega$. It turns out that for a large class of ideals it is possible to prove an analogue of Mathias' theorem, while for other ideals there _are_ definable infinite mad families. No characterization of when one or the other situation arises seems to be known at this time.
For more information, please contact Mathematics Department by phone at 626-395-4335 or by email at [email protected].