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