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