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Logic Seminar

Tuesday, May 22, 2018
1:00pm to 2:00pm
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Building 15, Room 131
The cohomology of the first omega alephs: some questions
Jeffrey Bergfalk, Department of Mathematics, Cornell University,
We describe the conversion of a ladder system on $\omega_n$ to a nonzero element of $\mathrm{H}^n(\omega_n)$ (computed with respect to a constant sheaf on $\omega_n$). In the case of $n=1$, this process of conversion is, simply, Todorcevic's technique of walks on the countable ordinals -- one which, ``[d]espite its simplicity [...] can be used to derive virtually all known other structures that have been defined so far on $\omega_1$'' (\textit{Walks on Ordinals}, 19). For higher $n$, this conversion plays a more prospective role, pointing to dramatically underexplored ZFC structures on higher $\omega_n$. Time permitting, we'll outline two questions in this area that we think of as \textit{next}.
For more information, please contact Mathematics Department by phone at 626-395-4335 or by email at [email protected].