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