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Hedetniemi's conjecture OCA Dowker space Forcing Axioms free Souslin tree Jonsson cardinal tensor product graph Aronszajn tree Erdos-Hajnal graphs Erdos Cardinal Singular cofinality Filter reflection Shelah's Strong Hypothesis Successor of Singular Cardinal C-sequence Cohen real Weakly compact cardinal Absoluteness Commutative cancellative semigroups PFA Intersection model Rado's conjecture Analytic sets Almost Souslin Singular cardinals combinatorics Uniformly homogeneous AIM forcing Small forcing Fast club SNR Whitehead Problem Rainbow sets Ineffable cardinal Coherent tree Kurepa Hypothesis nonmeager set Antichain Greatly Mahlo Martin's Axiom L-space free Boolean algebra Iterated forcing unbounded function weak diamond Diamond Slim tree middle diamond HOD Successor of Regular Cardinal GMA Minimal Walks Subtle cardinal Generalized Clubs regressive Souslin tree weak square Diamond-sharp xbox Ramsey theory over partitions Souslin Tree Generalized descriptive set theory Microscopic Approach specializable Souslin tree S-Space Almost countably chromatic Parameterized proxy principle Knaster and friends Forcing Diamond for trees Sigma-Prikry diamond star Subnormal ideal Closed coloring b-scale Was Ulam right Square-Brackets Partition Relations Nonspecial tree Distributive tree Commutative projection system Constructible Universe Subtle tree property Subadditive Well-behaved magma Ulam matrix Rock n' Roll Uniformly coherent ccc Luzin set incompactness Amenable C-sequence Prikry-type forcing Strong coloring Respecting tree Sierpinski's onto mapping principle transformations very good scale Singular Density square principles Local Club Condensation. Almost-disjoint family Reflecting stationary set Precaliber club_AD Poset Countryman line full tree PFA(S)[S] Vanishing levels Open Access Ostaszewski square stationary reflection Cardinal Invariants Club Guessing coloring number Prevalent singular cardinals higher Baire space countably metacompact Uniformization Chang's conjecture square ZFC construction positive partition relation Postprocessing function projective Boolean algebra sap Hindman's Theorem Hereditarily Lindelöf space Universal Sequences Fat stationary set Strongly compact cardinal P-Ideal Dichotomy strongly bounded groups Partition Relations Ascent Path Lipschitz reduction Foundations Mandelbrot set Cardinal function stick weak Kurepa tree Sakurai's Bell inequality Non-saturation Chromatic number reflection principles Dushnik-Miller indecomposable ultrafilter approachability ideal polarized partition relation Large Cardinals Knaster Strongly Luzin set Reduced Power Selective Ultrafilter Fodor-type reflection super-Souslin tree 54G20 O-space Axiom R stationary hitting
Tag Archives: Cohen real
On the ideal J[kappa]
Abstract. Motivated by a question from a recent paper by Gilton, Levine and Stejskalova, we obtain a new characterization of the ideal $J[\kappa]$, from which we confirm that $\kappa$-Souslin trees exist in various models of interest. As a corollary we … Continue reading
Posted in Publications, Souslin Hypothesis
Tagged Cardinal Invariants, Cohen real, nonmeager set
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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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An $S$-space from a Cohen real
Recall that an $S$-space is a regular hereditarily separable topological space which is not hereditarily Lindelöf. In this post, we shall establish the consistency of the existence of such a space. Theorem (Roitman, 1979). Let $\mathbb C=({}^{<\omega}\omega,\subseteq)$ be the notion of … Continue reading
