 Set Theory in the United Kingdom is a new joint research group
in set theory funded by the London
Mathematical Society (Scheme 3) with members at the Universities of
Bristol, Cambridge, East Anglia, Leeds, Oxford, Warwick and University
College London.
A preliminary meeting (STUK 0) of the joint research group was held
at the Royal Society in London
on 7 November 2018. The meeting in Cambridge on 16 February 2019
will be the group's first full meeting.
The meeting will take place in Meeting Room 13 at the
Centre for Mathematical Sciences (CMS) in Cambridge
(a useful map of the pavilions and meeting rooms at the CMS).
There will be two talks and ample time for informal presentations of
workinprogress and open problems.
  


Mirna Džamonja (Norwich & Paris)
Strong logics in set theory and search for singular compactness


Joel David Hamkins (Oxford)
Forcing as a computational process 
Abstract. In the world of infinite cardinals, combinatorial properties of singular
cardinals are somewhat special. This is especially visible by the fact that
they often exhibit a compactness behaviour, such as in Shelah's singular
compactness theorem or pcf theorem. The cardinal \(\aleph_0\) is also very
special, often because of the compactness. An important example is the
compactness of the first order logic. Therefore it is natural to ask if
there is a compact logic associated to singular cardinals, a question that
we explore. This talk reports on results in progress obtained jointly with
Jouko Väänänen.

Abstract. We investigate the senses in which settheoretic forcing can be
seen as a computational process on the models of set theory. Given an oracle
for the atomic or elementary diagram of a model of set theory \(\langle
M,\in^M\rangle\), for example, we explain senses in which one may compute
\(M\)generic filters \(G\subset P\in M\) and the corresponding forcing
extensions \(M[G]\). Meanwhile, no such computational process is functorial,
for there must always be isomorphic alternative presentations of the same
model of set theory \(M\) that lead by the computational process to
nonisomorphic forcing extensions \(M[G]\not\cong M[G']\). Indeed, there is no
Borel function providing generic filters that is functorial in this sense.
This is joint work with Russell Miller and Kameryn Williams.

11:30–12:15
 Welcome and informal discussions

CMS, Pav C Common Room


12:15–14:00
 Lunch
 Churchill College


14:00–15:00

Joel David Hamkins (Oxford)
Forcing as a computational process
 CMS, MR 13 (Pav E, lower level)


15:00–15:15

Break

CMS, Pav C Common Room


15:15–16:15

Mirna Džamonja (Norwich & Paris)
Strong logics in set theory and search for singular compactness
 CMS, MR 13 (Pav E, lower level)


16:15–16:30

Break

CMS, Pav C Common Room


16:30–18:30
 Informal session with presentation of workinprogress and open problems (5–15 minutes each):
16:30–16:40 Sam AdamDay (Amsterdam)
16:40–16:45 Nawaf Alsowait (Norwich)
16:45–16:50 Cristina Criste (Norwich)
16:50–17:05 Adam Epstein (Warwick)
17:05–17:20 Lorenzo Galeotti (Amsterdam & Hamburg)
17:20–17:40 Asaf Karagila (Norwich)
17:40–17:50 Philipp Schlicht (Bristol)
17:50–18:30 Time for informal discussions
 CMS, MR 13 (Pav E, lower level)



