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Logic Seminar - Pantelis Eleftheriou (Leeds)

Dates:12 October 2022
Times:15:15 - 16:15
What is it:Seminar
Organiser:Department of Mathematics
Who is it for:University staff, External researchers, Adults, Alumni, Current University students
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  • Department of Mathematics

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  • In category "Seminar"
  • In group "(Maths) Maths seminar series"
  • In group "(Maths) Logic"
  • By Department of Mathematics

Title: An unbounded version of Zarankiewicz's problem

Abstract: Zarankiewicz's problem for hypergraphs asks for upper bounds on the number of edges of a hypergraph that has no complete sub-hypergraphs of a given size. Let M be an o-minimal structure. Basit-Chernikov-Starchenko-Tao-Tran (2021) proved that the following are equivalent:

(1) "linear Zarankiewicz's bounds" hold for hypergraphs whose edge relation is induced by a fixed relation definable in M (2) M does not define an infinite field.

We prove that the following are equivalent:

(1') linear Zarankiewicz bounds hold for sufficiently "distant" hypergraphs whose edge relation is induced by a fixed relation definable in M (2') M does not define a full field (that is, one whose domain is the whole universe of M).

This is joint work (in progress) with Aris Papadopoulos.

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