
Set Theory in the United Kingdom is a research network in set theory
that was formed in 2018 and has been funded by two Scheme 3 grants of the London Mathematical Society and an INI Network Support grant
by the Isaac Newton Institute for Mathematical Sciences.
The members of the network are the Universities of Bristol, Cambridge, East Anglia,
Leeds, Oxford, Warwick and University College London. The current coordinators are
Andrew BrookeTaylor (Leeds) and Benedikt LĂ¶we (Cambridge).
STUK 10 is the tenth installment of the series and will take place in
Classroom 3 in the Andrew Wiles Building of the Mathematical
Institute of the University of Oxford (Woodstock Road, OX2 6GG; location information), Wednesday,
14 June 2023. The local organisers are Clara List, Emma Palmer, and Wojciech Wołoszyn.
Invited speakers:
11:00–12:00

Pimpen Vejjajiva (Bangkok):
Infinite factorials and related cardinals
Abstract.
A factorial \(\mathfrak{m}!\) is the cardinality of the set of permutations on a set
which is of cardinality \(\mathfrak{m}\). In this talk, I shall give relationships between some
cardinals related to infinite factorials in the absence of the Axiom of Choice.


12:00–13:30
 Lunch


13:30–14:30
 Joel David Hamkins (Notre Dame IN):
Set theory with abundant urelements
Abstract. I shall speak on the surprising strength of the secondorder
reflection principle in
the context of set theory with abundant urelements. The theory \(\mathsf{GBcU}\)
with the abundant urelement
axiom and secondorder reflection is biinterpretable with a strengthening of \(\mathsf{KM}\)
with a
supercompact cardinal. This is joint work with Bokai Yao.


14:30–14:45
 Coffee break


14:45–15:45

Grigor Sargsyan (Sopot):
Sealing theorems
Abstract. We will explore different types of SealingÂ Theorems (generic absoluteness
theorems), and will state a new one that seals the theory of \(\mathbf{L}(\mathrm{uB},
\mathbb{R})[\mathcal{C}]\) where \(\mathrm{uB}\) is the set of universally Baire sets and \(\mathcal{C}\) is the club filter on
\(\wp_{\omega_1}(\mathrm{uB})\). This is joint work with Sandra Müller.


15:45–16:00
 Coffee break


16:00–18:00
 Informal presentations
16:00–16:15. Andrew BrookeTaylor (Leeds).
16:15–16:45. Philipp Schlicht (Bristol).


