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