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very good scale Square-Brackets Partition Relations Countryman line super-Souslin tree Kurepa Hypothesis SNR Forcing Rock n' Roll sap Erdos-Hajnal graphs 54G20 Hindman's Theorem Axiom R stationary reflection Dowker space Forcing with side conditions Uniformly coherent Subadditive tensor product graph Precaliber Reduced Power P-Ideal Dichotomy Club Guessing Uniformization ccc Antichain Sierpinski's onto mapping principle specializable Souslin tree perfectly normal Lipschitz reduction Uniformly homogeneous Chromatic number approachability ideal b-scale Postprocessing function Shelah's Strong Hypothesis Cardinal function regressive Souslin tree Minimal Walks middle diamond Cardinal Invariants Successor of Singular Cardinal Open Access Iterated forcing Cohen real Fast club C-sequence unbounded function nonmeager set Slim tree Amenable C-sequence Distributive tree Rainbow sets Commutative cancellative semigroups Singular cofinality incompactness Almost Souslin Diamond for trees Sakurai's Bell inequality Strong coloring Generalized descriptive set theory coloring number Partition Relations Well-behaved magma L-space full tree Ulam matrix square Whitehead Problem Monotonically far Large Cardinals Chang's conjecture Almost-disjoint family Souslin Tree Prevalent singular cardinals Successor of Regular Cardinal Fodor-type reflection Fat stationary set square principles Forcing Axioms Diamond-sharp Analytic sets Erdos Cardinal Closed coloring Jonsson cardinal projective Boolean algebra Small forcing Reflecting stationary set Subtle tree property Strongly Luzin set Generalized Clubs GMA weak diamond strongly bounded groups Luzin set AIM forcing club_AD free Boolean algebra Hedetniemi's conjecture Universal Sequences Subtle cardinal Absoluteness Martin's Axiom weak Kurepa tree Ascent Path ZFC construction positive partition relation Diamond reflection principles Entangled linear order S-Space stationary hitting Prikry-type forcing Sigma-Prikry Ramsey theory over partitions diamond star Ascending path Dushnik-Miller transformations free Souslin tree Almost countably chromatic polarized partition relation Weakly compact cardinal Foundations Greatly Mahlo Aronszajn tree PFA(S)[S] Selective Ultrafilter Non-saturation Constructible Universe Ineffable cardinal Parameterized proxy principle Hereditarily Lindelöf space Ostaszewski square Commutative projection system Mandelbrot set HOD xbox Microscopic Approach Interval topology on trees Rado's conjecture Was Ulam right? Coherent tree Poset countably metacompact Knaster weak square Vanishing levels Filter reflection Respecting tree Subnormal ideal OCA Nonspecial tree O-space Singular Density Singular cardinals combinatorics Knaster and friends higher Baire space Intersection model Local Club Condensation. stick Strongly compact cardinal PFA indecomposable filter
Tag Archives: 03E57
Weak square and stationary reflection
Joint work with Gunter Fuchs. Abstract. It is well-known that the square principle $\square_\lambda$ entails the existence of a non-reflecting stationary subset of $\lambda^+$, whereas the weak square principle $\square^*_\lambda$ does not. Here we show that if $\mu^{cf(\lambda)}<\lambda$ for all $\mu<\lambda$, … Continue reading
Posted in Publications, Squares and Diamonds
Tagged 03E05, 03E35, 03E57, Diamond, Forcing Axioms, stationary reflection, weak square
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A forcing axiom deciding the generalized Souslin Hypothesis
Joint work with Chris Lambie-Hanson. Abstract. We derive a forcing axiom from the conjunction of square and diamond, and present a few applications, primary among them being the existence of super-Souslin trees. It follows that for every uncountable cardinal $\lambda$, … Continue reading
Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, 03E57, Diamond, Forcing Axioms, Souslin Tree, square, super-Souslin tree
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