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