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