Joint work with Alejandro Poveda and Dima Sinapova.
Abstract. We prove the consistency of the failure of the singular cardinals hypothesis at
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Amenable C-sequence Successor of Regular Cardinal reflection principles Slim tree Knaster Local Club Condensation. C-sequence unbounded function SNR 54G20 GMA Jonsson cardinal transformations Luzin set Cardinal Invariants Filter reflection Fat stationary set weak square Universal Sequences Commutative projection system full tree PFA(S)[S] Sigma-Prikry Square-Brackets Partition Relations very good scale polarized partition relation Generalized descriptive set theory diamond star Weakly compact cardinal Sakurai's Bell inequality countably metacompact nonmeager set Uniformly coherent S-Space Strongly compact cardinal Dowker space Erdos-Hajnal graphs sap Vanishing levels Nonspecial tree Chromatic number Knaster and friends stationary reflection Well-behaved magma Mandelbrot set Iterated forcing Absoluteness strongly bounded groups free Souslin tree Subnormal ideal Poset HOD projective Boolean algebra Uniformization OCA Diamond for trees free Boolean algebra tensor product graph Selective Ultrafilter Whitehead Problem Subadditive ccc higher Baire space Microscopic Approach Ineffable cardinal approachability ideal Shelah's Strong Hypothesis Prevalent singular cardinals weak diamond Open Access Axiom R Commutative cancellative semigroups Strong coloring Constructible Universe Foundations square Greatly Mahlo Lipschitz reduction Cohen real Erdos Cardinal Singular cofinality Antichain stationary hitting Almost-disjoint family Ramsey theory over partitions Subtle tree property xbox regressive Souslin tree Almost countably chromatic Parameterized proxy principle Cardinal function Kurepa Hypothesis square principles b-scale Diamond-sharp coloring number stick Fodor-type reflection Strongly Luzin set Singular Density incompactness middle diamond Closed coloring Generalized Clubs PFA Was Ulam right? Almost Souslin AIM forcing indecomposable filter Rado's conjecture Forcing club_AD Prikry-type forcing Non-saturation Aronszajn tree Chang's conjecture Rock n' Roll Postprocessing function Rainbow sets Successor of Singular Cardinal weak Kurepa tree Distributive tree Hedetniemi's conjecture ZFC construction Reflecting stationary set Ascent Path Club Guessing Martin's Axiom Intersection model Partition Relations L-space Small forcing Forcing Axioms Precaliber Diamond Large Cardinals Dushnik-Miller Hindman's Theorem Minimal Walks Ulam matrix Hereditarily Lindelöf space positive partition relation O-space Uniformly homogeneous Sierpinski's onto mapping principle Ostaszewski square P-Ideal Dichotomy super-Souslin tree Singular cardinals combinatorics Reduced Power Fast club Countryman line Analytic sets Coherent tree Subtle cardinal Respecting tree Souslin Tree specializable Souslin tree
Submitted to Advances in Mathematics, October 2021.
Accepted, October 2023.