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