Archives of: Prague Set Theory Seminar

Jan Grebik: Borel selectors of Borel ideals

Dear all,

The seminar meets on Wednesday October 18th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Jan Grebik — Borel selectors of Borel ideals
We present a result that there is an F_sigma ideal without Borel
selector and deduce that Galvin’s lemma does not have a “Borel proof.”
We also show that Nash-Williams theorem has a “Borel proof” and
therefore Galvin’s lemma is intrinsically more complex than
Nash-Williams theorem.

Best,
David

Saeed Ghasemi: Isomorphisms between reduced

Dear all,

The seminar meets on Wednesday October 11th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Saeed Ghasemi — Isomorphisms between reduced
products of matrices

The talk will be mostly based on the paper:
https://arxiv.org/abs/1310.1353

Best,
David

Boriša Kuzeljević: P-ideal dichotomy and the strong form of the Souslin hypothesis

Dear all,

The seminar meets on Wednesday October 4th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program:
Boriša Kuzeljević — P-ideal dichotomy and the strong form of the
Souslin hypothesis

Best,
David

Peter Vojtáš: Galois Tukey connections and reductions of (finite) combinatorial search problems

The seminar meets on Wednesday September 27th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program:
Peter Vojtáš — Galois Tukey connections and reductions of (finite)
combinatorial search problems

We start from paper of A. Blass Query-Answer category … and present
some results and problems connected to K. Weihrauch reduction from
constru

Miha Habič: The grounded Martin’s axiom

Dear all,

The seminar meets on Wednesday September 13th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program:
Miha Habič — The grounded Martin’s axiom

We will examine the notion of a grounded forcing axiom, which asserts
that the universe is a forcing extension by a forcing notion from a
particular class and that the usual forcing axiom holds for forcings
from that class coming from the ground model of the extension. We shall
focus in particular on the grounded Martin’s axiom, where the universe
is a ccc extension. The principle has some of the combinatorial strength
of MA, but allows for more flexibility (for example, a singular
continuum). Furthermore, it is more robust under mild forcing extensions
than full MA, since it is often preserved after adding a Cohen or a
random real. We will also briefly glance at grounded versions of other
forcing axioms, such as grounded PFA, and outline some open questions in
the area.

Best,
David

Stefan Hoffelner: NS saturated and Δ_1-definable

The seminar meets on Wednesday September 6th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program:
Stefan Hoffelner — NS saturated and Δ_1-definable

Abstract:
Questions which investigate the interplay of the saturation of the
nonstationary ideal on ω_1, NS, and definability properties of the
surrounding universe can yield surprising and deep results. Woodins
theorem that in a model with a measurable cardinal where NS is
saturated, CH must definably fail is the paradigmatic example. It is
another remarkable theorem of H. Woodin that given ω-many Woodin
cardinals there is a model in which NS is saturated and ω-dense, which
in particular implies that NS is (boldface) Δ_1-definable. The latter
statement is of considerable interest in the emerging field of
generalized descriptive set theory, as the club filter is known to
violate the Baire property.
With that being said the following question, asked first by S.D.
Friedman and L. Wu seems relevant: is it possible to construct a model
in which NS is both Δ_1-definable and saturated from less than ω-many
Woodins? In this talk I will outline a proof that this is indeed the
case: given the existence of M_1^#, there is a model of ZFC in which the
nonstationary ideal on ω_1 is saturated and Δ_1-definable with parameter
ω_1. In the course of the proof I will present a new coding technique
which seems to be quite suitable to obtain definability results in the
presence of iterated forcing constructions over inner models for large
cardinals.

Jindra Zapletal: Quotient forcings defined from group actions

Dear all,

The seminar meets on Wednesday July 12th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program:
Jindra Zapletal will talk about quotient forcings defined from group
actions.

Best,
David

Jindrich Zapletal: An interpreter for topologists

Wednesday, July 1, 2015, 11:00
Prague – IM AS CR, Zitna 25, seminar room, front building, third floor

Speaker: Jindrich Zapletal (University of Florida & IM CAS)

Title: An interpreter for topologists

Jan Grebik: Oscillations of reals and related forcings

Wednesday, May 20, 2015, 11:00
Prague – IM AS CR, Zitna 25, seminar room, front building, third floor

Speaker: Jan Grebik

Title: Oscillations of reals and related forcings

Abstract:

We will review results about oscillations of real numbers and properties of posets defined using oscillations.

Ali Enayat: Leibnizian motives in set theory

Wednesday, May 6, 2015, 11:00
Prague – IM AS CR, Zitna 25, seminar room, front building, third floor

Speaker: Ali Enayat (University of Gothenburg)

Title: Leibnizian motives in set theory

Abstract:

Leibniz’principle of identity of indiscernibles appears rather unrelated to set theory, but Mycielski (1995) formulated a set-theoretic principle P that captures the spirit of Leibniz’s principle in the following sense: P holds in a model M of ZF iff M is elementarily equivalent to a model M* in which there are no indiscernibles. In this talk I will discuss my work on Mycielski’s principle, including its relationship to the axiom of choice, and its equivalence (over ZF) with the global versions of the Kinna-Wagner selection principles.