There will be a series of Logic-related events in Cambridge starting on Wednesday 29th November and running into the weekend. Entirely by coincidence there are a lot of Clay lectures in Cambridge that same week.
The Logic-related events include:
The Absolute Arithmetic Continuum and The Unification of All Numbers Great and Small
The topological content of Monotone Bar Induction and the Fan Principle
Both MBI and FP are techniques used in some variant of constructive
mathematics. They also have some interest for proper mathematics. They
are often only applied only to the Baire tree and the Cantor tree,
respectively, but in a suitable form can be applied to any tree. In
the classical context they are choice principles related to Dependent
Choice. The two principles are not equivalent and the difference can
be measure using a tological ranking technique.
I will describe some of the older work on the techniques, and then throw in a new observation.
Boolean valued Models revisited
Substitution in Fraenkel-Mostowski sets
Stewart Shapiro: "The open-texture of
computability" (The paper is an attempt to apply Waismann's
notion of open-texture, and Lakatos's *Proofs and refutations*, to the
notion of computability, and thus to the question of whether Church's
thesis is subject to mathematical proof.) There is a handout
It will be held on Friday 1/xii in the Centre for Mathematical Sciences, Meeting Room 3, at the usual time of 1400hrs.
At 1100-1300 on Friday 1/xii Meeting Room 14, CMS, there will be a ``Part IV'' lecture on Quine's set theory NF by Thomas Forster. This is part of DPMMS's programme of lectures for graduates. This lecture will be devoted to background in NF, since I now have a Ph.D. student studying it.