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