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