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Local Club Condensation. Coherent tree Luzin set Ramsey theory over partitions Commutative cancellative semigroups HOD Subnormal ideal GMA Erdos Cardinal Interval topology on trees Uniformly homogeneous very good scale Respecting tree Commutative projection system Chromatic number xbox Prevalent singular cardinals Souslin Tree Cohen real Subtle tree property indecomposable filter Countryman line Postprocessing function Foundations tensor product graph Mandelbrot set sap Entangled linear order Selective Ultrafilter Filter reflection Analytic sets Shelah's Strong Hypothesis O-space Cardinal function full tree specializable Souslin tree 54G20 OCA polarized partition relation Singular cardinals combinatorics weak diamond Sigma-Prikry Hereditarily Lindelöf space ZFC construction Successor of Singular Cardinal Knaster and friends Cardinal Invariants positive partition relation Club Guessing Fat stationary set Almost Souslin Subtle cardinal Rock n' Roll Strongly Luzin set Uniformly coherent Lipschitz reduction Intersection model Microscopic Approach incompactness Ascent Path Subadditive Successor of Regular Cardinal Fast club Amenable C-sequence Antichain PFA(S)[S] reflection principles Open Access Sierpinski's onto mapping principle Hedetniemi's conjecture Jonsson cardinal Aronszajn tree square Forcing Axioms b-scale Precaliber L-space Constructible Universe Kurepa Hypothesis Partition relations for trees Uniformization Forcing perfectly normal Vanishing levels Generalized Clubs Minimal Walks Nonspecial tree Chang's conjecture club_AD P-Ideal Dichotomy C-sequence Small forcing Diamond for trees Greatly Mahlo Weakly compact cardinal Reflecting stationary set middle diamond projective Boolean algebra Almost countably chromatic Singular Density Was Ulam right? Absoluteness Well-behaved magma Dushnik-Miller Whitehead Problem free Boolean algebra Axiom R diamond star Strongly compact cardinal regressive Souslin tree Diamond-sharp Singular cofinality Reduced Power higher Baire space weak square PFA Square-Brackets Partition Relations weak Kurepa tree stationary hitting Ostaszewski square Ulam matrix Knaster Ascending path AIM forcing Closed coloring Rainbow sets Strong coloring Diamond Iterated forcing transformations countably metacompact Universal Sequences Sakurai's Bell inequality approachability ideal Poset Dowker space Rado's conjecture SNR Martin's Axiom Large Cardinals stick nonmeager set Parameterized proxy principle unbounded function Ineffable cardinal Generalized descriptive set theory Distributive tree Slim tree coloring number free Souslin tree S-Space stationary reflection Almost-disjoint family Forcing with side conditions Non-saturation Erdos-Hajnal graphs Partition Relations super-Souslin tree Fodor-type reflection Hindman's Theorem Monotonically far Prikry-type forcing strongly bounded groups ccc square principles
Tag Archives: 54D20
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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