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