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countably metacompact Prevalent singular cardinals Uniformization ZFC construction Cardinal Invariants P-Ideal Dichotomy specializable Souslin tree free Souslin tree Antichain regressive Souslin tree Amenable C-sequence Diamond for trees Small forcing weak diamond Ascent Path GMA Closed coloring Fodor-type reflection ccc Universal Sequences Uniformly homogeneous Knaster and friends Whitehead Problem projective Boolean algebra Forcing Axioms Chromatic number Successor of Singular Cardinal Erdos Cardinal PFA(S)[S] Martin's Axiom Singular cofinality Chang's conjecture polarized partition relation Precaliber Forcing Sierpinski's onto mapping principle Subtle cardinal Hereditarily Lindelöf space AIM forcing Nonspecial tree L-space Diamond-sharp Axiom R Postprocessing function Selective Ultrafilter square Knaster Sigma-Prikry Singular Density Strong coloring diamond star middle diamond Absoluteness C-sequence Ineffable cardinal Was Ulam right Cohen real positive partition relation Subadditive strongly bounded groups Hedetniemi's conjecture Square-Brackets Partition Relations Large Cardinals Partition Relations SNR Hindman's Theorem Ostaszewski square very good scale Non-saturation Ramsey theory over partitions xbox indecomposable ultrafilter unbounded function Mandelbrot set reflection principles Foundations Greatly Mahlo Filter reflection Prikry-type forcing stick Distributive tree Successor of Regular Cardinal sap Subtle tree property Strongly Luzin set Rainbow sets Cardinal function Rado's conjecture Fat stationary set Commutative cancellative semigroups Souslin Tree Constructible Universe Erdos-Hajnal graphs Dushnik-Miller tensor product graph Parameterized proxy principle Club Guessing weak square Slim tree b-scale Rock n' Roll free Boolean algebra approachability ideal stationary reflection Almost-disjoint family incompactness Generalized descriptive set theory 54G20 square principles Almost Souslin Iterated forcing Poset Kurepa Hypothesis Open Access Fast club Reduced Power coloring number Jonsson cardinal Well-behaved magma club_AD Local Club Condensation. Diamond Minimal Walks Generalized Clubs full tree Aronszajn tree OCA Subnormal ideal super-Souslin tree Lipschitz reduction Analytic sets PFA Luzin set transformations Uniformly coherent stationary hitting Vanishing levels Reflecting stationary set Coherent tree nonmeager set Dowker space Sakurai's Bell inequality Shelah's Strong Hypothesis higher Baire space Almost countably chromatic HOD Singular cardinals combinatorics weak Kurepa tree O-space Ulam matrix S-Space Weakly compact cardinal Microscopic Approach
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Full Souslin trees at small cardinals
Joint work with Shira Yadai and Zhixing You. Abstract. A $\kappa$-tree is full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full $\kappa$-Souslin tree may consistently exist. Shelah gave an affirmative … Continue reading
Posted in Preprints, Souslin Hypothesis
Tagged Diamond for trees, full tree, Greatly Mahlo, Microscopic Approach, Parameterized proxy principle, Subtle cardinal, tensor product graph
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