Logic Seminar

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series
24 April 2018
16:00
Philip Welch
Abstract

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.
 

1 May 2018
16:00
Boris Zilber
Abstract

I will present a variation of positive model theory which addresses the issues of approximations of conventional geometric structures by sequences of Zariski structures as well as approximation by sequences of finite structures. In particular I am interested in applications to quantum mechanics.

I will report on a progress in defining and calculating oscillating in- tegrals of importance in quantum physics. This is based on calculating Gauss sums of order higher or equal to 2 over rings Z/mfor very specific m

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