Gareth Boxall

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We consider the question of when an expansion of a topological structure has the property that every open set definable in the expansion is definable in the original structure. This question is related to and inspired by recent work of Dolich, Miller and Steinhorn on the property of having o-minimal open core. We answer the question in a fairly general(More)
Generalising work from [2] and [6], we give sufficient conditions for a theory TP to inherit NIP from T , where TP is an expansion of the theory T by a unary predicate P . We apply our result to theories, studied in [1], of the real field with a subgroup of the unit circle.
A new relation between morphisms in a category is introduced – roughly speaking (accurately in the categories Set and Top), f ‖ g iff morphisms w : dom(f) → dom(g) never map subobjects of fibres of f non-constantly to fibres of g. (In the algebraic setting replace fibre with kernel.) This relation and a slight weakening of it are used to define(More)
09h00 09h45 Zurab Janelidze Algebraic importance of “modus ponens” 09h50 10h20 Gareth Boxall NIP (Not the Independence Property) 10h25 10h55 James Gray Algebraic exponentiation 11h00 11h15 Tea/coffee Mathematics Tea Room 11h15 12h15 Alessandra Palmigiano Groupoid quantales beyond the étale setting 12h20 12h50 Willem Conradie Algorithmic canonicity and(More)
We study the notion of weak one-basedness introduced in recent work of Berenstein and Vassiliev. Our main results are that this notion characterises linearity in the setting of geometric þ-rank 1 structures and that lovely pairs of weakly one-based geometric þ-rank 1 structures are weakly one-based with respect to þ-independence. We also study geometries(More)
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