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