Archives
Keywords
Jonsson cardinal AIM forcing Dushnik-Miller Foundations Sigma-Prikry Entangled linear order club_AD Open Access Knaster Uniformly coherent Hereditarily Lindelöf space Countryman line Singular Density Kurepa Hypothesis Respecting tree Small forcing Singular cofinality Axiom R Partition Relations Sierpinski's onto mapping principle free Souslin tree Sakurai's Bell inequality Luzin set Whitehead Problem Generalized Clubs Closed coloring regressive Souslin tree Prevalent singular cardinals Strongly Luzin set Subtle cardinal Strongly compact cardinal Non-saturation OCA Precaliber GMA Erdos-Hajnal graphs SNR super-Souslin tree Diamond-sharp Cardinal function reflection principles Forcing Aronszajn tree weak diamond Commutative projection system Club Guessing sap Fast club S-Space Generalized descriptive set theory indecomposable filter Dowker space coloring number Diamond Cardinal Invariants very good scale Subnormal ideal weak Kurepa tree Diamond for trees stationary reflection Microscopic Approach Successor of Singular Cardinal Absoluteness Universal Sequences Analytic sets Ineffable cardinal ZFC construction b-scale perfectly normal Vanishing levels Was Ulam right? Cohen real Well-behaved magma stationary hitting Reduced Power Distributive tree Amenable C-sequence Ostaszewski square Souslin Tree Coherent tree Strong coloring Parameterized proxy principle Selective Ultrafilter Prikry-type forcing Singular cardinals combinatorics Ascent Path stick P-Ideal Dichotomy Large Cardinals Forcing with side conditions specializable Souslin tree Knaster and friends HOD Almost Souslin free Boolean algebra Subadditive ccc Lipschitz reduction Filter reflection projective Boolean algebra polarized partition relation Fat stationary set Commutative cancellative semigroups transformations Local Club Condensation. Chromatic number approachability ideal 54G20 Minimal Walks Rado's conjecture weak square Monotonically far Ramsey theory over partitions Shelah's Strong Hypothesis xbox Constructible Universe Weakly compact cardinal middle diamond Erdos Cardinal Rainbow sets strongly bounded groups Reflecting stationary set Successor of Regular Cardinal O-space Nonspecial tree Almost countably chromatic Ascending path PFA(S)[S] Partition relations for trees tensor product graph Fodor-type reflection Chang's conjecture square principles countably metacompact positive partition relation Slim tree Interval topology on trees Hindman's Theorem Mandelbrot set full tree Almost-disjoint family Antichain nonmeager set PFA Forcing Axioms Subtle tree property Square-Brackets Partition Relations incompactness Poset diamond star square Ulam matrix Hedetniemi's conjecture Martin's Axiom Postprocessing function Uniformization C-sequence higher Baire space unbounded function Uniformly homogeneous Greatly Mahlo Rock n' Roll Iterated forcing Intersection model L-space
Tag Archives: Respecting tree
Proxy principles in combinatorial set theory
Joint work with Ari Meir Brodsky and Shira Yadai. Abstract. The parameterized proxy principles were introduced by Brodsky and Rinot in a 2017 paper as new foundations for the construction of $\kappa$-Souslin trees in a uniform way that does not … 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
Square with built-in diamond-plus
Joint work with Ralf Schindler. Abstract. We formulate combinatorial principles that combine the square principle with various strong forms of diamond, and prove that the strongest amongst them holds in $L$ for every infinite cardinal. As an application, we prove that … Continue reading
Posted in Publications, Squares and Diamonds
Tagged 03E05, 03E45, Almost Souslin, diamond star, Kurepa Hypothesis, Minimal Walks, Respecting tree, square, xbox
1 Comment
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
