Set Theory in the UK is a nationwide seminar sponsored by the London Mathematical Society taking place 4 times per year in different locations. This program is aimed at increasing the sense of community of the set theoretic community in the UK and encourage collaborations.
The first meeting of 2020 will take place on 11 February, 2020, at the Brian Mercer Room in the Royal Society building: 6–9 Carlton House Terrace, London SW1Y 5AG.
Category theory suggests a viewpoint on many branches of mathematics, set theory included. I will attempt to explain that perspective and what it offers. This talk will mostly be an overview, and I will not assume knowledge of category theory beyond the definition of category.
We study non-Archimedean ordered fields with uncountable base number (the base number of an ordered field is the length of the shortest null sequence). We consider generalisations of the intermediate value theorem and the Bolzano-Weierstrass theorem for these fields and realise that these properties are in conflict with each other: saturation of the field is needed for (a reasonable version of) the intermediate value theorem, but implies that the standard Bolzano-Weierstrass property does not hold. We investigate weaker properties that are consistent with saturation and show that they are related to the tree property of the base number of the field. This is joint work with Carl, Galeotti, and Hanafi.