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