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