Archives
Keywords
transformations Closed coloring SNR Was Ulam right? Erdos-Hajnal graphs Cardinal Invariants Reduced Power Generalized descriptive set theory Local Club Condensation. polarized partition relation weak square diamond star Almost Souslin Square-Brackets Partition Relations Luzin set middle diamond Greatly Mahlo stick HOD Monotonically far Coherent tree C-sequence Analytic sets Reflecting stationary set Successor of Regular Cardinal Ineffable cardinal full tree Strongly Luzin set Sierpinski's onto mapping principle Minimal Walks Sigma-Prikry weak diamond free Boolean algebra Prevalent singular cardinals Entangled linear order Erdos Cardinal Rainbow sets Diamond-sharp Singular cofinality Partition relations for trees Commutative projection system Slim tree Singular cardinals combinatorics S-Space PFA(S)[S] Strong coloring Rado's conjecture Ascent Path sap Fast club Forcing Axioms Mandelbrot set Well-behaved magma higher Baire space Foundations Rock n' Roll Nonspecial tree Vanishing levels ccc Forcing with side conditions Selective Ultrafilter Hereditarily Lindelöf space Postprocessing function Souslin Tree Universal Sequences regressive Souslin tree Antichain OCA countably metacompact Aronszajn tree Cohen real Poset Iterated forcing Absoluteness b-scale Open Access Subtle cardinal GMA positive partition relation Commutative cancellative semigroups indecomposable filter Weakly compact cardinal Club Guessing Hedetniemi's conjecture Ascending path xbox Strongly compact cardinal free Souslin tree Subtle tree property Uniformly homogeneous Countryman line O-space approachability ideal Filter reflection very good scale Singular Density square Respecting tree Ulam matrix Sakurai's Bell inequality square principles Martin's Axiom P-Ideal Dichotomy Dowker space perfectly normal Fodor-type reflection super-Souslin tree Subadditive weak Kurepa tree Non-saturation projective Boolean algebra PFA Successor of Singular Cardinal strongly bounded groups Whitehead Problem Parameterized proxy principle Intersection model Uniformization coloring number Uniformly coherent 54G20 Diamond for trees Kurepa Hypothesis Diamond Shelah's Strong Hypothesis Dushnik-Miller Axiom R Ostaszewski square Chang's conjecture nonmeager set Precaliber tensor product graph Cardinal function AIM forcing Jonsson cardinal Fat stationary set Microscopic Approach Almost-disjoint family Prikry-type forcing specializable Souslin tree ZFC construction Partition Relations Lipschitz reduction Subnormal ideal Ramsey theory over partitions Small forcing Knaster and friends L-space Forcing Constructible Universe club_AD Hindman's Theorem reflection principles Chromatic number Interval topology on trees Amenable C-sequence stationary reflection stationary hitting Generalized Clubs Almost countably chromatic unbounded function Large Cardinals incompactness Knaster Distributive tree
Tag Archives: Ascent Path
A new model for all C-sequences are trivial
Joint work with Zhixing You and Jiachen Yuan. Abstract. We construct a model in which all C-sequences are trivial, yet there exists a $\kappa$-Souslin tree with full vanishing levels. This answers a question from a previous paper, and provides an … Continue reading
Posted in Compactness, Publications
Tagged Ascent Path, C-sequence, Intersection model, Souslin Tree, Subtle tree property, Vanishing levels
2 Comments
Ketonen’s question and other cardinal sins
Joint work with Zhixing You and Jiachen Yuan. Abstract. Answering a question of Ketonen from the late 1970’s, it is proved that a weakly compact cardinal carrying an indecomposable ultrafilter need not be measurable. The result is obtained by analyzing … 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
2 Comments
Knaster and friends III: Subadditive colorings
Joint work with Chris Lambie-Hanson. Abstract. We continue our study of strongly unbounded colorings, this time focusing on subadditive maps. In Part I of this series, we showed that, for many pairs of infinite cardinals $\theta < \kappa$, the existence … Continue reading
A microscopic approach to Souslin-tree constructions. Part II
Joint work with Ari Meir Brodsky. Abstract. In Part I of this series, we presented the microscopic approach to Souslin-tree constructions, and argued that all known $\diamondsuit$-based constructions of Souslin trees with various additional properties may be rendered as applications of … Continue reading
Reduced powers of Souslin trees
Joint work with Ari Meir Brodsky. Abstract. We study the relationship between a $\kappa$-Souslin tree $T$ and its reduced powers $T^\theta/\mathcal U$. Previous works addressed this problem from the viewpoint of a single power $\theta$, whereas here, tools are developed … Continue reading
