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