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Fodor-type reflection Almost Souslin Weakly compact cardinal Cohen real diamond star Ulam matrix Singular cofinality club_AD Slim tree specializable Souslin tree Small forcing indecomposable filter Chromatic number nonmeager set Fast club Singular Density Selective Ultrafilter Successor of Singular Cardinal strongly bounded groups xbox Commutative projection system Knaster and friends Chang's conjecture unbounded function Cardinal Invariants stationary hitting Countryman line Sakurai's Bell inequality Sierpinski's onto mapping principle Precaliber Ascent Path Jonsson cardinal super-Souslin tree Subtle cardinal positive partition relation Generalized descriptive set theory Ineffable cardinal Fat stationary set Reduced Power transformations Prikry-type forcing Microscopic Approach Hedetniemi's conjecture Luzin set Cardinal function Uniformization Distributive tree Hereditarily Lindelöf space Rock n' Roll Poset Greatly Mahlo Absoluteness Whitehead Problem Respecting tree PFA Parameterized proxy principle ZFC construction Successor of Regular Cardinal OCA HOD AIM forcing weak diamond regressive Souslin tree Non-saturation perfectly normal Erdos Cardinal middle diamond free Boolean algebra incompactness Subtle tree property higher Baire space Analytic sets Partition relations for trees Vanishing levels Partition Relations O-space Dushnik-Miller Diamond for trees Was Ulam right? square Ostaszewski square Diamond Intersection model stationary reflection Club Guessing Aronszajn tree Subnormal ideal square principles Filter reflection Uniformly homogeneous Commutative cancellative semigroups Forcing with side conditions Shelah's Strong Hypothesis Universal Sequences Almost countably chromatic Forcing b-scale Rainbow sets ccc Strongly compact cardinal Entangled linear order Almost-disjoint family 54G20 Closed coloring Kurepa Hypothesis C-sequence free Souslin tree Souslin Tree weak square Diamond-sharp Ascending path Lipschitz reduction Interval topology on trees Amenable C-sequence Nonspecial tree stick Foundations Forcing Axioms Axiom R Rado's conjecture approachability ideal Uniformly coherent Erdos-Hajnal graphs Antichain Local Club Condensation. SNR Martin's Axiom Hindman's Theorem coloring number Mandelbrot set Generalized Clubs countably metacompact full tree Postprocessing function Reflecting stationary set polarized partition relation Sigma-Prikry Prevalent singular cardinals Ramsey theory over partitions reflection principles PFA(S)[S] S-Space Large Cardinals Open Access Strongly Luzin set GMA Monotonically far Strong coloring projective Boolean algebra Coherent tree very good scale Well-behaved magma sap Subadditive Constructible Universe Singular cardinals combinatorics L-space Square-Brackets Partition Relations Dowker space Knaster Iterated forcing Minimal Walks P-Ideal Dichotomy weak Kurepa tree tensor product graph
Tag Archives: Luzin set
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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