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Gareth Boxall - The definable (p,q) conjecture and distality

Dates:12 February 2020
Times:15:00 - 16:00
What is it:Seminar
Organiser:Department of Mathematics
Who is it for:University staff, External researchers, Current University students
Speaker:Gareth Boxall
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  • Department of Mathematics

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

Gareth Boxall joins us for the logic seminar

The definable (p,q) conjecture for NIP theories is so called on account of a connection with a theorem in combinatorics which I shall discuss. In model theoretic terms, it concerns a property that non-forking formulas might possess in the NIP setting. Say we have a model M of an NIP theory T, a sufficiently saturated elementary extension N and a formula phi(x,b) with parameter b. Consider the family of formulas {phi(x,b'):q(b')} obtained by allowing b' to range over the set of all realisations in N of the type q(y) of b over M. If this family is finitely consistent then, according to the conjecture, there is a formula psi(y) in q(y) such that {phi(x,b'):psi(b')} is also finitely consistent.

Chernikov and Simon asked if this is true, it having long been known for stable theories. Various special cases are known. I shall discuss these, focusing on the case of distal NIP theories which was established by Charlotte Kestner and me.

Speaker

Gareth Boxall

Organisation: Stellenbosch University

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Omar Leon Sanchez

omar.sanchez@manchester.ac.uk

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