Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 17 October 2018, 17:00 hrs
Room: S17#04-05, Department of Mathematics, NUS
Speaker: Dilip Raghavan
Title: Order dimension
Abstract: We will present some results on the order dimension of
various partial orders, focusing on partial orders which are locally countable.
This is joint work with Kojiro Higuchi, Steffen Lempp and Frank Stephan.
Talk held by Monroe Eskew (KGRC) at the KGRC seminar on 2018-10-18.
Abstract: Using ideas from Foreman-Magidor-Shelah, one can force from a Woodin cardinal to show it is consistent that the nonstationary ideal on $\omega_1$ is saturated while the quotient boolean algebra is rigid. The key is to apply Martin’s Axiom to the almost-disjoint coding forcing to see how it interacts with a generic elementary embedding. This strategy requires the continuum hypothesis to fail. Towards showing the consistency of rigid ideals with GCH, the speaker investigated other coding strategies: stationary coding (with Brent Cody), a rigid version of the Levy collapse, and ladder-system coding (in recent work with Paul Larson). We have some equiconsistencies about rigid ideals on $\omega_1$ and $\omega_2$, as well as some global possibilities from very large cardinals. Some natural questions remain about $\omega_1$ and successors of singulars.
Research seminar, Kurt Gödel Research Center – Thursday, October 11th
Abstract: I will give a full proof of a joint result with O. Guzman regarding a
technique for destroying P-ultrafilters with Silver forcing. Time
permitting, I will present several applications.
Research seminar, Kurt Gödel Research Center – October 9th
Abstract: Least fixed points of monotone operators are well-studied objects in many
areas of mathematical logic. Typically, they are characterized as the
intersection of all sets closed under the respective operator or as the
result of its iteration from below.
In this talk I will start off from specific $\Sigma_1$ operators in a
Kripke-Platek environment and relate fixed point assertions to alternative
set existence principles. By doing that, we are also led to some
“largeness axioms” and to several open problems.
Seminar: Working group in applications of set theory, IMPAN
Thursday, 11.10. 2018, 10:15, room 105, IMPAN
Speaker: Piotr Koszmider (IMPAN)
Title: “Uncountable constructions from CH using generic filters”
Abstact. We will present some old CH constructions due to S. Shelah. As usual they use transfinie induction, diagonalization and enumeration of all relevant objects in the first uncountable type. However, the use of the Martin’s axiom type arguments makes them additionally powerful.
Visit our seminar page which may include some future talks at https://www.impan.pl/~set_theory/Seminar/
Mathematical logic seminar – Oct 9 2018
Time: 3:30pm – 4:30 pm
Room: Wean Hall 8220
Speaker: Clinton Conley
Department of Mathematical Sciences
Title: Realizing abstract systems of congruence II
An abstract system of congruence (ASC) is simply an equivalence relation
on the power set of a finite set F satisfying some nondegeneracy
conditions. Given such an ASC and an action of a group G on a set X, a
realization of the ASC is a partition of X into pieces indexed by F such
that whenever two subsets A, B are asc-equivalent, the corresponding
subsets XA and XB of X can be translated to one another in the action.
Familiar notions like paradoxical decompositions can be easily formalized
and refined by the ASC language. Wagon, upon isolating this notion,
characterized those ASCs which can be realized by rotations of the sphere.
He asks whether there is an analogous characterization for realizing ASCs
using partitions with the property of Baire. We provide such a
characterization. This is joint work with Andrew Marks and Spencer Unger.
The seminar meets on Wednesday October 10th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Note that there will be no seminar on Wednesday October 17th.
Program: Miha Habič — Surgery and generic coding
There has been some interest recently in nonamalgamability phenomena
between countable models of set theory, and forcing extensions of a
fixed model in particular. Nonamalgamability is typically achieved by
coding some forbidden object between a collection of models in such a
way that each model on its own remains oblivious, but some combination
of them can recover the forbidden information.
In this talk we will examine the problem of coding arbitrary information
into a generic filter, focusing on two particular examples. First, I
will present some results of joint work with Jonathan Verner where we
consider surgical modifications to Cohen reals and sets of indices where
such modifications are always possible. Later, I will discuss a recent
result of S. Friedman and Hathaway where they achieve, using different
coding, nonamalgamability between arbitrary countable models of set
theory of the same height.
Posted in Seminars
Tagged Miha Habic
Talk held by David Fernández-Bretón (KGRC) at the KGRC seminar on 2018-10-04. The recorded talk is available here.
Abstract: In the absence of the Axiom of Choice, there may be infinite sets for which certain Ramsey-theoretic statements – such as Ramsey’s or (appropriately phrased) Hindman’s theorem – fail. In this talk, we will analyse the existence of such sets, and their precise location within the hierarchy of infinite Dedekind-finite sets; independence proofs will be carried out using the Fränkel-Mostowski technique of permutation models.
This is joint work with Joshua Brot and Mengyang Cao.
Tuesday, October 9, 2018, 15.00
Howard House 4th Floor Seminar Room, University of Bristol
Speaker: Gabriel Fernandes (University of Münster)
Title: Tall cardinals in extender models
Gitik proved under ¬0^sword that if κ is a measurable cardinal and 2^κ > λ ≥ κ^+ and λ is a regular cardinal then o^K(κ) ≥ λ, where K stands for the core model. In joint work with Ralf Schindler, in a attempt to generalize Gitik’s result to larger core models, we obtained for the case where V is an extender model a characterization of λ-tall cardinals in terms of the function o^K(). In the talk I will define λ-tall cardinals, o^K(), give an informal definition of the core model, state precisely the characterization we obtained and sketch its proof.