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PFA Cardinal function Parameterized proxy principle Countryman line square higher Baire space stationary reflection Almost-disjoint family Erdos Cardinal Ramsey theory over partitions Martin's Axiom Antichain reflection principles Iterated forcing very good scale Mandelbrot set Square-Brackets Partition Relations Partition Relations Minimal Walks incompactness Subnormal ideal Lipschitz reduction Chromatic number stick strongly bounded groups Aronszajn tree weak Kurepa tree GMA Rock n' Roll specializable Souslin tree indecomposable ultrafilter Non-saturation Sakurai's Bell inequality ZFC construction Chang's conjecture PFA(S)[S] Knaster and friends 54G20 square principles b-scale Successor of Regular Cardinal super-Souslin tree Uniformly coherent Shelah's Strong Hypothesis full tree tensor product graph diamond star S-Space Diamond Intersection model Sierpinski's onto mapping principle approachability ideal unbounded function ccc Rado's conjecture Precaliber Generalized Clubs Axiom R Universal Sequences C-sequence Constructible Universe Diamond for trees Uniformization Fast club Small forcing Filter reflection Singular Density Reflecting stationary set free Souslin tree xbox Knaster Analytic sets Open Access Singular cardinals combinatorics weak diamond Coherent tree Ostaszewski square Generalized descriptive set theory Luzin set AIM forcing Prevalent singular cardinals countably metacompact P-Ideal Dichotomy Commutative cancellative semigroups Uniformly homogeneous Slim tree Subadditive Ulam matrix Fat stationary set projective Boolean algebra Closed coloring Cardinal Invariants SNR Prikry-type forcing Large Cardinals Subtle cardinal club_AD polarized partition relation Microscopic Approach coloring number Club Guessing Strongly compact cardinal Distributive tree Was Ulam right Commutative projection system Jonsson cardinal Absoluteness Singular cofinality nonmeager set HOD Dushnik-Miller transformations Forcing Axioms L-space Poset regressive Souslin tree sap Diamond-sharp Fodor-type reflection Vanishing levels Ineffable cardinal Hindman's Theorem Local Club Condensation. Strong coloring Kurepa Hypothesis positive partition relation Souslin Tree O-space Amenable C-sequence Sigma-Prikry Erdos-Hajnal graphs Rainbow sets free Boolean algebra Hereditarily Lindelöf space Subtle tree property Greatly Mahlo stationary hitting Nonspecial tree Postprocessing function OCA Respecting tree Selective Ultrafilter Almost Souslin weak square Well-behaved magma Reduced Power Cohen real Foundations Weakly compact cardinal Whitehead Problem Forcing Ascent Path middle diamond Strongly Luzin set Almost countably chromatic Dowker space Hedetniemi's conjecture Successor of Singular Cardinal
Category Archives: Invited Talks
11th Young Set Theory Workshop, June 2018
I gave a 4-lecture tutorial at the 11th Young Set Theory Workshop, Lausanne, June 2018. Title: In praise of C-sequences. Abstract. Ulam and Solovay showed that any stationary set may be split into two. Is it also the case that … Continue reading
Posted in Invited Talks
Tagged Aronszajn tree, C-sequence, incompactness, Knaster, Minimal Walks, Postprocessing function, square
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The 14th International Workshop on Set Theory in Luminy, October 2017
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
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
