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