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Tuesday, 25 February 2025 - 10:00 to 11:30 <br />
Place: IM, konÃrna
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Speaker: Maximilian Hadek, Univerzita Karlova<br />
Title: A compactness lemma for Ramsey categories
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Abstract <br />
<p><br></p><p> K\H{o}nig's tree lemma is a classical tool for compactness arguments, though it is flawed, useless in uncountable settings and restricted by the inherent linearity of trees. </p><p>We prove a categorical generalization of K\H{o}nig's lemma that aims to circumvent these issues and discuss its applications to Ramsey theory, as it turns out a category is Ramsey if and only if the lemma holds there. As an example of how to use the lemma, we give an elegant proof of the existence of canonical functions between Ramsey structures.</p>
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For more information see the seminar web page at <br />
https://www.math.cas.cz/index.php/events/seminar/6
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Set Theory and Analysis mailing list <br />
settfa@math.cas.cz <br />
https://list.math.cas.cz/listinfo/settfa@math.cas.cz
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