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Partition Relations club_AD stick Strongly Luzin set OCA middle diamond Dushnik-Miller Precaliber higher Baire space weak square Distributive tree PFA Nonspecial tree Generalized Clubs Singular Density Sierpinski's onto mapping principle Selective Ultrafilter Club Guessing Martin's Axiom Uniformization Sakurai's Bell inequality Souslin Tree Commutative cancellative semigroups Reduced Power Fat stationary set Shelah's Strong Hypothesis ZFC construction Ineffable cardinal Cardinal function Ramsey theory over partitions Foundations diamond star full tree ccc Vanishing levels weak diamond Closed coloring HOD reflection principles Forcing Ostaszewski square transformations Rock n' Roll Subtle tree property Dowker space tensor product graph Hindman's Theorem Almost Souslin positive partition relation nonmeager set Almost-disjoint family Filter reflection Coherent tree C-sequence Open Access Erdos Cardinal strongly bounded groups Luzin set Iterated forcing O-space sap Antichain free Boolean algebra Cohen real Hedetniemi's conjecture Axiom R Mandelbrot set Successor of Regular Cardinal Subtle cardinal Small forcing Weakly compact cardinal weak Kurepa tree countably metacompact Ulam matrix polarized partition relation Reflecting stationary set Diamond-sharp Diamond 54G20 Kurepa Hypothesis Rainbow sets Jonsson cardinal Minimal Walks Local Club Condensation. coloring number Erdos-Hajnal graphs Square-Brackets Partition Relations xbox Universal Sequences Absoluteness L-space Lipschitz reduction Microscopic Approach P-Ideal Dichotomy Slim tree Large Cardinals Uniformly coherent S-Space b-scale Aronszajn tree super-Souslin tree Almost countably chromatic Hereditarily Lindelöf space incompactness Subnormal ideal Analytic sets Non-saturation approachability ideal Whitehead Problem Prikry-type forcing SNR Poset Uniformly homogeneous Parameterized proxy principle Chang's conjecture projective Boolean algebra Strong coloring Singular cofinality regressive Souslin tree square Fast club Knaster Constructible Universe stationary hitting AIM forcing Chromatic number free Souslin tree specializable Souslin tree Greatly Mahlo Knaster and friends Ascent Path Cardinal Invariants Postprocessing function Was Ulam right unbounded function Successor of Singular Cardinal Diamond for trees indecomposable ultrafilter Forcing Axioms Singular cardinals combinatorics Amenable C-sequence Generalized descriptive set theory very good scale Fodor-type reflection Rado's conjecture GMA Prevalent singular cardinals square principles stationary reflection Subadditive PFA(S)[S] Sigma-Prikry Well-behaved magma
Blog Archives
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
The eightfold way
Joint work with James Cummings, Sy-David Friedman, Menachem Magidor, and Dima Sinapova. Abstract. Three central combinatorial properties in set theory are the tree property, the approachability property and stationary reflection. We prove the mutual independence of these properties by showing … Continue reading
Ordinal definable subsets of singular cardinals
Joint work with James Cummings, Sy-David Friedman, Menachem Magidor, and Dima Sinapova. Abstract. A remarkable result by Shelah states that if $\kappa$ is a singular strong limit cardinal of uncountable cofinality then there is a subset $x$ of $\kappa$ such … Continue reading
Posted in Publications, Singular Cardinals Combinatorics
Tagged AIM forcing, HOD, Singular cardinals combinatorics
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