### Archives

### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- Generalizations 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

### Keywords

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

# Category Archives: Invited Talks

## The 14th International Workshop on Set Theory in Luminy

I gave an invited talk at the 14th International Workshop on Set Theory in Luminy in Marseille, October 2017. Talk Title: Distributive Aronszajn trees Abstract: It is well-known that that the statement “all $\aleph_1$-Aronszajn trees are special” is consistent with ZFC … Continue reading

Posted in Invited Talks, Squares and Diamonds
Tagged Aronszajn tree, Postprocessing function
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## 6th European Set Theory Conference, July 2017

I gave a 3-lecture tutorial at the 6th European Set Theory Conference in Budapest, July 2017. Title: Strong colorings and their applications. Abstract. Consider the following questions. Is the product of two $\kappa$-cc partial orders again $\kappa$-cc? Does there exist … Continue reading

Posted in Invited Talks, Open Problems
Tagged b-scale, Cohen real, Luzin set, Minimal Walks, Souslin Tree, Square-Brackets Partition Relations
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## ASL North American Meeting, March 2017

I gave a plenary talk at the 2017 ASL North American Meeting in Boise, March 2017. Talk Title: The current state of the Souslin problem. Abstract: Recall that the real line is that unique separable, dense linear ordering with no endpoints in … Continue reading

## MFO workshop in Set Theory, February 2017

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

## MFO workshop in Set Theory, January 2014

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: