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Logic seminar

usually takes place each Monday at 16:00 in IM, rear building, ground floor
Chair: Pavel Pudlak, Neil Thapen, Jan Krajíček
More information on the old seminar web page. The programme is announced via the mailing list.

TBA

Emil Jeřábek
IM CAS
Monday, 24. October 2022 - 16:00 to 17:30
TBA

TBA

Emil Jeřábek
IM CAS
Monday, 17. October 2022 - 16:00 to 17:30
TBA

Compactness and incompactness in set theory, with applications to uncountable graphs

Chris Lambie-Hanson
IM CAS
Monday, 26. September 2022 - 16:00 to 17:30
(Joint seminar with set theory group)

The study of compactness phenomena at uncountable cardinals has been a central line of research in combinatorial set theory since the mid-twentieth century. In the first part of this talk, we will give a broad overview of this area of research and survey some of its most prominent results. We will then look at a few recent results concerning compactness phenomena for uncountable graphs. We first look at possible generalizations of the de Bruijn-Erdos compactness theorem for chromatic numbers to uncountable cardinalities, in particular showing that consistently there are large uncountable graphs witnessing extreme failures of compactness for, e.g., the property of having a countable chromatic number. We then turn to the study of the structure of the collections of finite subgraphs of uncountably chromatic graphs, answering a question of Erdos, Hajnal, and Szemeredi about the growth rates of chromatic numbers in such collections of... more

On the Conjectures of Razborov and Rudich

Rahul Santhanam
University of Oxford
Monday, 23. May 2022 - 16:00 to 17:30
We say that Rudich's Conjecture holds for a propositional proof system Q if there are no efficient Q-proofs of random truth table tautologies. We say that Razborov's Conjecture holds for a propositional proof system Q if there are no efficient Q-proofs of any truth table tautologies. A fundamental task in proof complexity and the meta-mathematics of circuit lower bounds is to understand for which Q these conjectures hold. We show various results about these conjectures, including evidence for their difficulty.

Based on joint work with Jan Pich.

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