Workshop on
Combinatorial set theory and forcing theory
November 16 - 19, 2009
at Rakuyu Kaikan, Kyoto University, Japan
-
Aspero, David /
Forcing consequences of PFA together with the continuum large
slides
- Bice, Tristan /
Cardinal Invariants of Projections in the Calkin Algebra
slides
-
Farah, Ilijas /
All automorphisms of all Calkin algebras
By results of Philips-Weaver and myself,
the assertion that all automorphisms of the Calkin
algebra associated with a separable Hilbert space
are inner is independent from the usual axioms of
set theory. In these talks I will discuss the existence
of outer automorphisms of nonseparable Calkin algebras.
This is a joint work with Ernest Schimmerling and
Paul McKenney.
slides 1,
slides 1.5,
slides 2,
slides 3
-
Friedman, Sy-David /
Forcing, combinatorics and definability
In this three-lecture tutorial I will discuss the following topics,
concerned with the application of forcing to combinatorial and
definability-theoretic problems in set theory.
1. Definable wellorders
2. Cardinal Characteristics on uncountable cardinals
3. Models of BPFA
slides
-
Fujita, Hiroshi /
The $\sigma$-ideal of stoutly meager sets
-
Khomskii, Yurii /
Polarized partition properties on the second
level of the projective hierarchy
slides
-
Larson, Paul /
Universally measurable sets
-
Minami, Hiroaki /
Mathias-Prikry type forcing and dominating real
slides
- Miyamoto, Tadatoshi /
On the consistency strength of the FRP for the second uncountable cardinal
-
Nguyen Van The, Lionel /
On a problem of Specker about Euclidean representations of finite graphs
Say that a graph G is representable in dimension n if there is an embedding of G in the n-dimensional Euclidean space together with two distinct distances a and b such that under the embedding, all edges have length a and all non-edges have length b. The purpose of this talk is twofold. First, we will show that if G is finite and neither complete nor independent, then it is representable in dimension |G|-2. We will then present finer results due to Roy.
manuscript
-
Raghavan, Dilip /
A model with no strongly separable MAD families
slides
-
Sakai, Hiroshi /
On precipitousness of normal ideals
slides
- Usuba, Toshimichi /
Guessing sequences and indescribable cardinals
We study club guessing sequences on indescribable cardinals.
We show the consistency of the following statements:
1. kappa is indescribable and
there is no club guessing sequences on the set of
regular cardinals less than kappa.
2. kappa is indescribable and
the ideal over kappa defined by club guessing
sequences is saturated.
These contrast with well-known results that
some large cardinals imply the diamond principle, and
refute the saturation property of small ideals.
slides
-
Velickovic, Boban /
Long Ehrenfeucht Fraisse games and forcing