Scott Mutchnik : The Koponen Conjecture, part two

Posted by Scott Mutchnik , part of the Logic Seminar.

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March 6, 2024, 4 p.m.

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Abstract

We continue the proof of the first implication of the Koponen conjecture, showing that countably categorical n-ary simple theories are supersimple. Then we give our own proof, based on arguments of Palacín, that countably categorical, n-ary supersimple theories must have finite rank, using a quantity, F_Mb, that is in a certain sense dual to Freitag and Moosa’s degree of nonminimality. We also explain Tomašić and Wagner’s result on pseudolinearity, which depending on the strength used, either proves the implication from finite rank to one-based for omega-categorical n-ary theories, or proves the full implication from supersimple to one-based. If time permits, we explain the connection to some open questions on F_Mb. This is on joint work with John Baldwin and James Freitag.