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