Joint work with Roy Shalev and Stevo Todorcevic.
Abstract. It is proved that if there exists a Luzin set, or if either the stick principle or
In particular, any of the above hypotheses entails the existence of a Dowker space of size
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Subtle cardinal Singular Density Open Access polarized partition relation indecomposable ultrafilter incompactness tensor product graph Mandelbrot set regressive Souslin tree Coherent tree approachability ideal Hindman's Theorem S-Space Club Guessing Ramsey theory over partitions nonmeager set Well-behaved magma sap SNR HOD Aronszajn tree AIM forcing reflection principles Fast club Singular cardinals combinatorics Knaster and friends Closed coloring Almost-disjoint family Filter reflection square principles very good scale Subtle tree property Successor of Regular Cardinal Fat stationary set Commutative projection system square club_AD Uniformization Whitehead Problem Dowker space O-space stick Reduced Power 54G20 Postprocessing function Dushnik-Miller Ostaszewski square Subnormal ideal Axiom R Partition Relations Ulam matrix weak square Parameterized proxy principle OCA P-Ideal Dichotomy Sakurai's Bell inequality Cardinal function Antichain Forcing free Souslin tree PFA unbounded function Diamond Knaster Square-Brackets Partition Relations Prevalent singular cardinals weak Kurepa tree stationary hitting ccc PFA(S)[S] Precaliber Analytic sets Generalized descriptive set theory Erdos-Hajnal graphs Ineffable cardinal Nonspecial tree Hedetniemi's conjecture Luzin set Large Cardinals Poset L-space Diamond for trees Chromatic number super-Souslin tree Microscopic Approach Lipschitz reduction Sigma-Prikry Successor of Singular Cardinal countably metacompact Uniformly coherent higher Baire space Chang's conjecture Greatly Mahlo Sierpinski's onto mapping principle diamond star Shelah's Strong Hypothesis Weakly compact cardinal Jonsson cardinal Hereditarily Lindelöf space Intersection model Erdos Cardinal Diamond-sharp Kurepa Hypothesis weak diamond C-sequence Strongly compact cardinal Prikry-type forcing Cohen real Cardinal Invariants free Boolean algebra Amenable C-sequence coloring number Uniformly homogeneous Distributive tree ZFC construction Rainbow sets Souslin Tree Reflecting stationary set Fodor-type reflection Foundations Ascent Path projective Boolean algebra Singular cofinality Respecting tree Forcing Axioms specializable Souslin tree Subadditive Was Ulam right? Strongly Luzin set Slim tree Rado's conjecture b-scale Local Club Condensation. Minimal Walks strongly bounded groups Almost Souslin Strong coloring Non-saturation Almost countably chromatic full tree Universal Sequences transformations GMA positive partition relation Countryman line Iterated forcing Generalized Clubs Commutative cancellative semigroups stationary reflection middle diamond xbox Selective Ultrafilter Constructible Universe Small forcing Rock n' Roll Vanishing levels Martin's Axiom Absoluteness
Submitted to Periodica Mathematica Hungarica, April 2022.
Accepted, December 2022.