### Archives

### Recent blog posts

- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- Genearlizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- Happy new jewish year! September 24, 2014
- Square principles April 19, 2014
- Partitioning the club guessing January 22, 2014

### Keywords

L-space Forcing Axioms Microscopic Approach Hereditarily Lindelöf space diamond star Partition Relations S-Space very good scale weak diamond Aronszajn tree Small forcing Dushnik-Miller Cardinal Invariants Mandelbrot set Absoluteness Almost-disjoint famiy Parameterized proxy principle tensor product graph Foundations xbox Hedetniemi's conjecture Almost Souslin free Boolean algebra Martin's Axiom Slim tree Universal Sequences Axiom R Fat stationary set Commutative cancellative semigroups Shelah's Strong Hypothesis sap ccc Chang's conjecture Singular Density Uniformization Knaster Singular cardinals combinatorics Successor of Regular Cardinal Cohen real Ostaszewski square approachability ideal Fodor-type reflection Singular coﬁnality Prevalent singular cardinals Rock n' Roll PFA(S)[S] Hindman's Theorem stationary reflection Jonsson cardinal square P-Ideal Dichotomy Chromatic number middle diamond Souslin Tree 11P99 projective Boolean algebra Kurepa Hypothesis Selective Ultrafilter Non-saturation Prikry-type forcing 20M14 Minimal Walks stationary hitting Erdos-Hajnal graphs reflection principles Club Guessing Weakly compact cardinal Forcing HOD Poset coloring number Successor of Singular Cardinal Constructible Universe polarized partition relation OCA Almost countably chromatic Cardinal function PFA Singular Cofinality Fast club Square-Brackets Partition Relations Rado's conjecture Rainbow sets Diamond b-scale 05A17 Coherent tree Large Cardinals weak square incompactness Ascent Path Erdos Cardinal Antichain Reduced Power Generalized Clubs 05D10 Sakurai's Bell inequality Whitehead Problem Stevo Todorcevic

# Category Archives: Invited Talks

## 2017 Workshop in Set Theory, Oberwolfach

I gave an invited talk at the Set Theory workshop in Obwerwolfach, February 2017. Talk Title: Coloring vs. Chromatic. Abstract: In a joint work with Chris Lambie-Hanson, we study the interaction between compactness for the chromatic number (of graphs) and … Continue reading

Posted in Invited Talks
Tagged Chromatic number, coloring number, incompactness, stationary reflection
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## Set Theory and its Applications in Topology, September 2016

I gave an invited talk at the Set Theory and its Applications in Topology meeting, Oaxaca, September 11-16, 2016. The talk was on the $\aleph_2$-Souslin problem. If you are interested in seeing the effect of a jet lag, the video is … Continue reading

## P.O.I. Workshop in pure and descriptive set theory, September 2015

I gave an invited talk at the P.O.I Workshop in pure and descriptive set theory, Torino, September 26, 2015. Title: $\aleph_3$-trees. Abstract: We inspect the constructions of four quite different $\aleph_3$-Souslin trees.

## The Apter-Gitik birthday conference, May 2015

I give an invited (blackboard) talk at the Apter-Gitik birthday conference, Carnegie Mellon University, May 30-31 2015. Title: Putting a diamond inside the square. Abstract: By a 35-year-old theorem of Shelah, $\square_\lambda+\diamondsuit(\lambda^+)$ does not imply square-with-built-in-diamond_lambda for regular uncountable cardinals … Continue reading

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## Forcing and its Applications Retrospective Workshop, April 2015

I gave an invited talk at Forcing and its Applications Retrospective Workshop, Toronto, April 1st, 2015. Title: A microscopic approach to Souslin trees constructions Abstract: We present an approach to construct $\kappa$-Souslin trees that is insensitive to the identity of … Continue reading

Posted in Invited Talks
Tagged Microscopic Approach, Parameterized proxy principle, Souslin Tree
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## INFTY Final Conference, March 2014

I gave an invited talk at the INFTY Final Conference meeting, Bonn, March 4-7, 2014. [Curiosity: Georg Cantor was born March 3, 1845] Title: Same Graph, Different Universe. Abstract: In a paper from 1998, answering a question of Hajnal, Soukup … Continue reading

## 2014 Workshop in Set Theory, Oberwolfach

I gave an invited talk at the Set Theory workshop in Obwerwolfach, January 2014. Talk Title: Complicated Colorings. Abstract: If $\lambda,\kappa$ are regular cardinals, $\lambda>\kappa^+$, and $E^{\lambda}_{\ge\kappa}$ admits a nonreflecting stationary set, then $\text{Pr}_1(\lambda,\lambda,\lambda,\kappa)$ holds. Downloads:

## Mathematics Colloquium, Bar-Ilan University, November 2013

I gave a colloquium talk at Bar-Ilan University on November 10, 2013. Title: Forcing as a tool to prove theorems Abstract: Paul Cohen celebrated solution to Hilbert’s first problem showed that the Continuum Hypothesis is independent of the usual axioms of … Continue reading

## 2013 Set Theory Programme on Large Cardinals and Forcing

I gave an invited talk at the Large Cardinals and Forcing meeting, Erwin Schrödinger International Institute for Mathematical Physics, Vienna, September 23–27, 2013. Talk Title: Hedetniemi’s conjecture for uncountable graphs Abstract: It is proved that in Godel’s constructible universe, for … Continue reading

Posted in Invited Talks
Tagged Almost countably chromatic, Chromatic number, Hedetniemi's conjecture
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## 2012 North American Annual Meeting of the ASL

I gave a special session talk at the ASL 2012 North American Annual Meeting (Madison, March 31–April 3, 2012). Talk Title: The extent of the failure of Ramsey’s theorem at successor cardinals. Extended abstract: Ramsey’s theorem asserts that for every coloring … Continue reading

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