### 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
- 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
- Partitioning the club guessing January 22, 2014

### Keywords

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

# 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: