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Fat stationary set positive partition relation weak diamond Iterated forcing Slim tree strongly bounded groups sap Vanishing levels Diamond Precaliber Knaster and friends Aronszajn tree Respecting tree Poset Dowker space Erdos Cardinal Sierpinski's onto mapping principle countably metacompact Hedetniemi's conjecture Cardinal function Strong coloring unbounded function Ascending path Uniformly coherent Interval topology on trees Singular Density Singular cardinals combinatorics square Cohen real OCA nonmeager set Parameterized proxy principle C-sequence Small forcing perfectly normal Hindman's Theorem Rainbow sets Uniformly homogeneous Coherent tree Souslin Tree free Boolean algebra Square-Brackets Partition Relations Generalized descriptive set theory higher Baire space Kurepa Hypothesis specializable Souslin tree Local Club Condensation. Generalized Clubs Almost-disjoint family Postprocessing function S-Space stationary hitting P-Ideal Dichotomy Luzin set Open Access Nonspecial tree Uniformization Ulam matrix diamond star Cardinal Invariants Ascent Path Fast club Diamond-sharp Diamond for trees Analytic sets approachability ideal Chang's conjecture Mandelbrot set Prikry-type forcing L-space Prevalent singular cardinals HOD Rock n' Roll Amenable C-sequence square principles Closed coloring Subadditive Forcing Axioms b-scale Successor of Singular Cardinal ccc coloring number Well-behaved magma reflection principles weak square ZFC construction GMA Was Ulam right? Singular cofinality Subtle cardinal PFA(S)[S] stick Monotonically far super-Souslin tree Forcing Successor of Regular Cardinal Erdos-Hajnal graphs regressive Souslin tree Distributive tree Selective Ultrafilter Constructible Universe Weakly compact cardinal Chromatic number Ramsey theory over partitions Sigma-Prikry Filter reflection Subtle tree property projective Boolean algebra SNR Entangled linear order Intersection model Shelah's Strong Hypothesis Almost countably chromatic Axiom R Reduced Power Almost Souslin Ineffable cardinal Commutative projection system Fodor-type reflection Dushnik-Miller Knaster Sakurai's Bell inequality full tree Martin's Axiom O-space weak Kurepa tree Greatly Mahlo Rado's conjecture 54G20 Countryman line Lipschitz reduction Hereditarily Lindelöf space polarized partition relation Minimal Walks Forcing with side conditions Universal Sequences indecomposable filter middle diamond Strongly Luzin set Ostaszewski square Club Guessing Reflecting stationary set Non-saturation Commutative cancellative semigroups PFA Whitehead Problem Subnormal ideal tensor product graph Partition Relations incompactness Antichain very good scale free Souslin tree Microscopic Approach Strongly compact cardinal AIM forcing Absoluteness Foundations stationary reflection Jonsson cardinal Large Cardinals transformations club_AD xbox
Tag Archives: countably metacompact
The power of trees
Joint work with Ari Meir Brodsky and Shira Yadai. Abstract. We give two consistent constructions of trees $T$ whose finite power $T^{n+1}$ is sharply different from $T^n$: An $\aleph_1$-tree $T$ whose interval topology $X_T$ is perfectly normal, but $(X_T)^2$ is … Continue reading →
Posted in Publications, Topology
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Tagged 03E35, 54B10, 54D15, 54D20, 54F05, Almost Souslin, countably metacompact, diamond star, Interval topology on trees, Nonspecial tree, Parameterized proxy principle, perfectly normal
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1 Comment
Diamond on ladder systems and countably metacompact topological spaces
Joint work with Rodrigo Rey Carvalho and Tanmay Inamdar. Abstract. Leiderman and Szeptycki proved that a single Cohen real introduces a ladder system $L$ over $\aleph_1$ for which the space $X_L$ is not a $\Delta$-space. They asked whether there is … Continue reading →
Posted in Preprints, Topology
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Tagged 03E05, 54G20, C-sequence, countably metacompact, Diamond, middle diamond, Open Access, weak diamond, ZFC construction
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3 Comments
A new small Dowker space
Joint work with Roy Shalev and Stevo Todorcevic. Abstract. It is proved that if there exists a Luzin set, or if either the stick principle or $\diamondsuit(\mathfrak b)$ hold, then an instance of the guessing principle $\clubsuit_{AD}$ holds at the … Continue reading →
Posted in Squares and Diamonds, Topology
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Tagged club_AD, countably metacompact, Dowker space, Luzin set, stick
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1 Comment
A guessing principle from a Souslin tree, with applications to topology
Joint work with Roy Shalev. Abstract. We introduce a new combinatorial principle which we call $\clubsuit_{AD}$. This principle asserts the existence of a certain multi-ladder system with guessing and almost-disjointness features, and is shown to be sufficient for carrying out … Continue reading →
Posted in Publications, Souslin Hypothesis, Topology
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Tagged club_AD, countably metacompact, Dowker space, O-space, regressive Souslin tree, S-Space, Souslin Tree, Vanishing levels
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2 Comments
