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