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