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club_AD Sakurai's Bell inequality Analytic sets Cardinal function free Souslin tree Martin's Axiom Respecting tree square principles Amenable C-sequence Cardinal Invariants Parameterized proxy principle Souslin Tree nonmeager set Erdos-Hajnal graphs Forcing Axioms weak Kurepa tree Mandelbrot set Closed coloring super-Souslin tree weak square Erdos Cardinal Fast club full tree Well-behaved magma Large Cardinals Knaster and friends Lipschitz reduction Reflecting stationary set Almost Souslin Ineffable cardinal Subnormal ideal Diamond Microscopic Approach tensor product graph ccc diamond star Rock n' Roll stick Singular cofinality Sigma-Prikry Dowker space Prevalent singular cardinals weak diamond Subtle cardinal P-Ideal Dichotomy Shelah's Strong Hypothesis Uniformly coherent Absoluteness Fodor-type reflection Constructible Universe square reflection principles Ramsey theory over partitions Hereditarily Lindelöf space Aronszajn tree b-scale Ascending path Ulam matrix Universal Sequences Coherent tree Almost-disjoint family ZFC construction Filter reflection Foundations Club Guessing countably metacompact Small forcing Ostaszewski square strongly bounded groups approachability ideal Antichain Diamond-sharp higher Baire space Whitehead Problem sap Local Club Condensation. Forcing with side conditions Entangled linear order Intersection model Interval topology on trees SNR Sierpinski's onto mapping principle Greatly Mahlo Cohen real Uniformly homogeneous Nonspecial tree positive partition relation Vanishing levels PFA Poset Almost countably chromatic Iterated forcing L-space perfectly normal Luzin set unbounded function 54G20 Rainbow sets Successor of Regular Cardinal Knaster Reduced Power Selective Ultrafilter AIM forcing Subtle tree property Hindman's Theorem Subadditive Monotonically far Open Access polarized partition relation Countryman line Forcing Slim tree Hedetniemi's conjecture regressive Souslin tree xbox Weakly compact cardinal coloring number specializable Souslin tree Precaliber Chromatic number Successor of Singular Cardinal Diamond for trees Generalized Clubs Jonsson cardinal Ascent Path GMA projective Boolean algebra Square-Brackets Partition Relations Singular cardinals combinatorics transformations middle diamond Strong coloring Postprocessing function Singular Density O-space HOD Rado's conjecture Commutative projection system Strongly compact cardinal Chang's conjecture PFA(S)[S] stationary hitting C-sequence Commutative cancellative semigroups Fat stationary set Kurepa Hypothesis incompactness Non-saturation OCA Partition Relations Distributive tree very good scale S-Space Generalized descriptive set theory Minimal Walks Was Ulam right? Uniformization stationary reflection free Boolean algebra indecomposable filter Axiom R Strongly Luzin set Partition relations for trees Prikry-type forcing Dushnik-Miller
Tag Archives: Sigma-Prikry
Sigma-Prikry forcing III: Down to Aleph_omega
Joint work with Alejandro Poveda and Dima Sinapova. Abstract. We prove the consistency of the failure of the singular cardinals hypothesis at $\aleph_\omega$ together with the reflection of all stationary subsets of $\aleph_{\omega+1}$. This shows that two classical results of … Continue reading
Sigma-Prikry forcing II: Iteration Scheme
Joint work with Alejandro Poveda and Dima Sinapova. Abstract. In Part I of this series, we introduced a class of notions of forcing which we call $\Sigma$-Prikry, and showed that many of the known Prikry-type notions of forcing that centers … Continue reading
Sigma-Prikry forcing I: The Axioms
Joint work with Alejandro Poveda and Dima Sinapova. Abstract. We introduce a class of notions of forcing which we call $\Sigma$-Prikry, and show that many of the known Prikry-type notions of forcing that centers around singular cardinals of countable cofinality … Continue reading
