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