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nonmeager set Singular cofinality Singular cardinals combinatorics Rado's conjecture Cardinal function Countryman line Successor of Regular Cardinal Almost countably chromatic OCA Sakurai's Bell inequality Lipschitz reduction Erdos-Hajnal graphs Kurepa Hypothesis Weakly compact cardinal Sierpinski's onto mapping principle Rock n' Roll Small forcing Aronszajn tree diamond star tensor product graph Fat stationary set Chang's conjecture club_AD Prevalent singular cardinals Iterated forcing stick Club Guessing Subtle cardinal Microscopic Approach Slim tree Uniformization Dushnik-Miller Vanishing levels Respecting tree Non-saturation Diamond-sharp Dowker space free Souslin tree coloring number Chromatic number Ostaszewski square Jonsson cardinal sap Selective Ultrafilter Constructible Universe S-Space Nonspecial tree P-Ideal Dichotomy full tree Strong coloring Ramsey theory over partitions super-Souslin tree unbounded function Cardinal Invariants stationary hitting Analytic sets 54G20 square principles Absoluteness Cohen real SNR positive partition relation weak Kurepa tree Diamond Sigma-Prikry middle diamond C-sequence Hereditarily Lindelöf space square Coherent tree Generalized Clubs Subnormal ideal AIM forcing Rainbow sets Ulam matrix L-space Subtle tree property Uniformly homogeneous Fast club incompactness Well-behaved magma regressive Souslin tree Subadditive projective Boolean algebra Foundations specializable Souslin tree Martin's Axiom Erdos Cardinal Souslin Tree Amenable C-sequence Interval topology on trees Was Ulam right? Fodor-type reflection Parameterized proxy principle Strongly compact cardinal Ascending path Shelah's Strong Hypothesis Square-Brackets Partition Relations Greatly Mahlo Minimal Walks Whitehead Problem Hedetniemi's conjecture Generalized descriptive set theory GMA countably metacompact perfectly normal weak diamond Local Club Condensation. Open Access Forcing Luzin set Forcing Axioms ccc Knaster indecomposable filter Postprocessing function Monotonically far PFA(S)[S] Reflecting stationary set Entangled linear order Diamond for trees Precaliber weak square Distributive tree approachability ideal Prikry-type forcing Commutative cancellative semigroups stationary reflection Almost-disjoint family Filter reflection Reduced Power higher Baire space Ascent Path polarized partition relation Partition Relations ZFC construction transformations Antichain Knaster and friends Axiom R Mandelbrot set reflection principles HOD Singular Density Poset Uniformly coherent Forcing with side conditions Commutative projection system Hindman's Theorem Universal Sequences Ineffable cardinal Strongly Luzin set O-space free Boolean algebra b-scale PFA Successor of Singular Cardinal strongly bounded groups Closed coloring Almost Souslin very good scale xbox Large Cardinals Intersection model
Tag Archives: weak Kurepa tree
Diamond on Kurepa trees
Joint work with Ziemek Kostana and Saharon Shelah. Abstract. We introduce a new weak variation of diamond that is meant to guess only the branches of a Kurepa tree. We demonstrate that this variation is considerably weaker than diamond by … Continue reading
Squares, ultrafilters and forcing axioms
Joint work with Chris Lambie-Hanson and Jing Zhang. Abstract. We study the interplay of the three families of combinatorial objects or principles. Specifically, we show the following. Strong forcing axioms, in general incompatible with the existence of indexed squares, can … Continue reading
The vanishing levels of a tree
Joint work with Shira Yadai and Zhixing You. Abstract. We initiate the study of the spectrum of sets that can be realized as the vanishing levels $V(\mathbf T)$ of a normal $\kappa$-tree $\mathbf T$. This is an invariant in the … Continue reading
Posted in Preprints, Souslin Hypothesis
Tagged Almost-disjoint family, Ascent Path, C-sequence, Coherent tree, Dowker space, Open Access, Parameterized proxy principle, regressive Souslin tree, Respecting tree, Subtle tree property, Uniformly homogeneous, Vanishing levels, weak Kurepa tree
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Sums of triples in Abelian groups
Joint work with Ido Feldman. Abstract. Motivated by a problem in additive Ramsey theory, we extend Todorcevic’s partitions of three-dimensional combinatorial cubes to handle additional three-dimensional objects. As a corollary, we get that if the continuum hypothesis fails, then for … Continue reading
