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

Dates: | 12 February 2020 |
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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 |

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