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