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