Archives of: Michigan Logic Seminar

David Fernández Bretón: An introduction to weak diamonds

Thursday, November 5, 2015, 16:00-17:30, 3096 East Hall.

I will introduce the basics of weak diamond principles, and show their usage with a couple of examples (construction of a Suslin tree and of a P-point).

Andrés Caicedo: The Haddad-Sabbagh results in the partition calculus of small countable ordinals, II

Thursday, October 22, 1015 — 16:00 to 17:30 — East Hall 3096

We present the second part of a survey of results announced 45 years ago by Haddad and Sabbagh on the partition calculus of ordinals. Part of the interest in these results is that they are obtained by reducing genuine infinitary combinatorics problems to purely finite (albeit unfeasible) ones.

Andrés Caicedo: The Haddad-Sabbagh results in the partition calculus of small countable ordinals

Wednesday, October 7, 16:00 to 17:30 in 3096 East Hall

We present a survey of results announced 45 years ago by Haddad and Sabbagh on the partition calculus of ordinals. Part of the interest in these results is that they are obtained by reducing genuine infinitary combinatorics problems to purely finite (albeit unfeasible) ones.

David Fernandez Breton: All that there is to know about gruff ultrafilters, II

Wednesday, September 23, 2015 — 16:00 to 17:30 — 3096 East Hall

An ultrafilter on the rational numbers is gruff if it has a base of perfect (this is, closed and without isolated points) sets. This definition, as well as the (still open) question of whether these objects exist, are due to van Douwen. We will present a completion of last time’s almost proof that b=c implies the existence of a gruff ultrafilter, and afterwards we will show that in Miller’s model there are gruff ultrafilters as well.

David Fernández Bretón: All that there is to know about gruff ultrafilters

Wednesday, September 16, 2015

3096 East Hall

16:00-17:30.

Gruff ultrafilters are ultrafilters on the rational numbers that have a basis of perfect sets (according to the usual Euclidean topology). I will explain what is known about their existence, and hopefully (if there’s enough time) finish with a theorem of M. Hrusak and myself that these ultrafilters exist in Miller’s model.

Andreas Blass: Partition Theorems and Ultrafilters Part 5

Monday, April 16, 2012, from 4 to 5:30pm
East Hall, room 2866

Speaker: Andreas Blass (University of Michigan)

Title: Partition Theorems and Ultrafilters Part 4

Abstract:

I’ll discuss a forcing notion that adjoins an ultrafilter that (1) is not a P-point, (2) has the strongest square-bracket partition property consistent with not being a P-point, and (3) is not a sum of other ultrafilters.

Andreas Blass: Partition Theorems and Ultrafilters Part 4

Monday, April 9, 2012, from 4 to 5:30pm
East Hall, room 2866

Speaker: Andreas Blass (University of Michigan)

Title: Ultrafilters and Partition Relations

Abstract:

I’ll finish the proof of the partition theorem for selective-indexed sums of non-isomorphic selective ultrafilters. Then I’ll describe a forcing that produces ultrafilters that have the same partition properties but are not sums and not P-points.

Blass_Ult+PartRel_part4

Andreas Blass: Partition Theorems and Ultrafilters Part 3

Monday, April 2, 2012, from 4 to 5:30pm
East Hall, room 2866

Speaker: Andreas Blass (University of Michigan)

Title: Ultrafilters and Partition Theorems

Abstract:

I’ll continue the series of talks on partition theorems and ultrafilters.

Blass_Ult+PartRel_part3

Andreas Blass: Partition Theorems and Ultrafilters Part 2

Monday, March 19, 2012, from 4 to 5:30pm
East Hall, room 2866

Speaker: Andreas Blass (University of Michigan)

Title: Partition Theorems and Ultrafilters Part 2

Abstract:

I’ll continue to speak on “Partition theorems and ultrafilters”.

Blass_Ult+PartRel_part2

Andreas Blass: Partition Theorems and Ultrafilters Part 1

Monday, March 12, 2012, from 4 to 5:30pm
East Hall, room 2866

Speaker: Andreas Blass (University of Michigan)

Title: Partition Theorems and Ultrafilters

Abstract:

My long-term goal is to discuss a notion of forcing that produces an ultrafilter on the natural numbers that (1) is not a P-point but (2) has the strongest partition properties that are possible subject to (1). These generic ultrafilters have properties similar to those of a sum of non-isomorphic selective ultrafilters indexed by a selective ultrafilter. Nevertheless, they are not sums. My short-term goal is to define and explain the concepts used here — partition properties, P-points, selective ultrafilters, and sums.

Blass_Ult+PartRel_part1