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