Logic Seminar

The logic seminar is given by invited speakers from across the UK and abroad who present recent research in the field. It is organised by Prof Jochen Koenigsmann. The talks are usually on Thursdays at 5:30pm in L6. Sometimes the logic and number theory groups hold a joint seminar.

24 April 2018
Philip Welch

We reflect on the set-theoretic ineffability of the Cantorian Absolute of all sets. If this is done in the style of Levy and Montague in a first order manner, or Bernays using second or higher order methods this has only resulted in principles that can justify large cardinals that are `intra-constructible', that is they do not contradict the assumption that V, the universe of sets of mathematical discourse, is Gödel's universe of constructible sets, namely L.  Peter Koellner has advanced reasons that this style of reflection will only have this rather limited strength. However set theorists would dearly like to have much stronger axioms of infinity. We propose a widened structural `Global Reflection Principle' that is based on a view of sets and Cantorian absolute infinities that delivers a proper class of Woodin cardinals (and more). A mereological view of classes is used to differentiate between sets and classes. Once allied to a wider view of structural reflection, stronger conclusions are thus possible.

Obtaining Woodin's Cardinals

P. D. Welch, in ``Logic in Harvard: Conference celebrating the birthday of Hugh Woodin''
Eds. A. Caicedo, J. Cummings, P.Koellner & P. Larson, AMS Series, Contemporary Mathematics, vol. 690, 161-176,May 2017.

Global Reflection principles, 

           P. D. Welch, currently in the Isaac Newton Institute pre-print series, No. NI12051-SAS, 
to appear as part of the Harvard ``Exploring the Frontiers of Incompleteness'' Series volume, 201?, Ed. P. Koellner, pp28.

In recent times, there have been more collaborative efforts between the logic group and the ComLab, both in terms of research and holding seminars. In particular, the OASIS seminar is host to speakers that both model-theorists and those working in the ComLab find interesting.

Advanced Logic Class

The advanced logic class is usually held on Thursdays at 11am in C5. It typically provides a forum for current PhD students and postdocs to present work in progress, or to work through important papers and digest recent advances in the subject. Prof Boris Zilber is in charge of these classes.

There are no seminars currently scheduled for this series.

Junior Logic Seminar

These seminars are highly informal and are given by graduate students in the logic group to each other (though all are welcome). The current organiser is Alfons Ruiz Guido. The seminars this term are at 5pm on Mondays in L3.