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