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strongly bounded groups Ascent Path incompactness Constructible Universe Antichain Fat stationary set Sierpinski's onto mapping principle Analytic sets Diamond Uniformization Dushnik-Miller transformations Almost countably chromatic Minimal Walks Jonsson cardinal Selective Ultrafilter Singular cofinality Rock n' Roll Vanishing levels Subtle cardinal Distributive tree Cohen real Was Ulam right Erdos-Hajnal graphs OCA middle diamond square Aronszajn tree C-sequence Dowker space Uniformly homogeneous coloring number Diamond-sharp super-Souslin tree Reflecting stationary set approachability ideal Cardinal Invariants Ulam matrix Well-behaved magma free Souslin tree stationary hitting Singular Density GMA polarized partition relation Iterated forcing Chang's conjecture free Boolean algebra Whitehead Problem Prevalent singular cardinals Club Guessing very good scale Non-saturation Coherent tree Lipschitz reduction Greatly Mahlo weak square stationary reflection Poset Parameterized proxy principle square principles sap Almost Souslin unbounded function Forcing ZFC construction Nonspecial tree Luzin set b-scale Singular cardinals combinatorics club_AD ccc Ramsey theory over partitions Sakurai's Bell inequality Fast club Successor of Regular Cardinal Diamond for trees Generalized descriptive set theory weak diamond Almost-disjoint family Hereditarily Lindelöf space Subadditive Universal Sequences Prikry-type forcing Subtle tree property Erdos Cardinal Slim tree Hedetniemi's conjecture Filter reflection Rado's conjecture Ostaszewski square Closed coloring indecomposable ultrafilter Kurepa Hypothesis tensor product graph Cardinal function PFA(S)[S] P-Ideal Dichotomy Mandelbrot set Local Club Condensation. Sigma-Prikry Strongly Luzin set full tree Uniformly coherent higher Baire space Hindman's Theorem Successor of Singular Cardinal Fodor-type reflection xbox stick Open Access weak Kurepa tree positive partition relation Souslin Tree Reduced Power HOD PFA specializable Souslin tree Small forcing Chromatic number Martin's Axiom reflection principles 54G20 Absoluteness Amenable C-sequence Rainbow sets Foundations Forcing Axioms diamond star Axiom R Generalized Clubs Weakly compact cardinal Precaliber Ineffable cardinal Square-Brackets Partition Relations AIM forcing regressive Souslin tree Knaster S-Space Subnormal ideal Strong coloring L-space nonmeager set SNR O-space Knaster and friends Large Cardinals Commutative cancellative semigroups Partition Relations countably metacompact Microscopic Approach Shelah's Strong Hypothesis Postprocessing function projective Boolean algebra
Tag Archives: Luzin set
A new small Dowker space
Joint work with Roy Shalev and Stevo Todorcevic. Abstract. It is proved that if there exists a Luzin set, or if either the stick principle or $\diamondsuit(\mathfrak b)$ hold, then an instance of the guessing principle $\clubsuit_{AD}$ holds at the … Continue reading
Ramsey theory over partitions III: Strongly Luzin sets and partition relations
Joint work with Menachem Kojman and Juris Steprāns. Abstract. The strongest type of coloring of pairs of countable ordinals, gotten by Todorcevic from a strongly Luzin set, is shown to be equivalent to the existence of a nonmeager set of … 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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