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