Joint work with Rodrigo Rey Carvalho and Tanmay Inamdar.
Abstract. Leiderman and Szeptycki proved that a single Cohen real introduces a ladder system
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Rado's conjecture diamond star ccc higher Baire space Hereditarily Lindelöf space Weakly compact cardinal xbox Whitehead Problem PFA(S)[S] Ascent Path Greatly Mahlo Amenable C-sequence Well-behaved magma Small forcing Intersection model 54G20 Hindman's Theorem Fat stationary set weak Kurepa tree Successor of Regular Cardinal countably metacompact Respecting tree Hedetniemi's conjecture square principles weak diamond Almost-disjoint family unbounded function specializable Souslin tree ZFC construction OCA square Successor of Singular Cardinal Subtle cardinal Strongly Luzin set Open Access Ineffable cardinal Subadditive Cardinal function stationary hitting Subtle tree property strongly bounded groups Slim tree Cardinal Invariants Almost Souslin Countryman line Uniformly homogeneous Antichain Erdos-Hajnal graphs C-sequence Aronszajn tree Dowker space Generalized Clubs approachability ideal Diamond for trees Singular cardinals combinatorics Rainbow sets Jonsson cardinal Postprocessing function projective Boolean algebra Shelah's Strong Hypothesis Chromatic number Strongly compact cardinal Sakurai's Bell inequality Sierpinski's onto mapping principle PFA Poset positive partition relation Axiom R Fodor-type reflection Parameterized proxy principle Diamond Iterated forcing Non-saturation Coherent tree Prikry-type forcing Strong coloring coloring number Subnormal ideal Rock n' Roll Kurepa Hypothesis Lipschitz reduction tensor product graph indecomposable filter middle diamond Was Ulam right? stick GMA full tree polarized partition relation Ulam matrix AIM forcing weak square L-space Uniformly coherent Absoluteness Diamond-sharp very good scale Commutative cancellative semigroups Cohen real Vanishing levels SNR b-scale club_AD Nonspecial tree free Souslin tree Local Club Condensation. Reduced Power Closed coloring Knaster Ostaszewski square Dushnik-Miller Forcing Axioms Foundations sap Erdos Cardinal P-Ideal Dichotomy Singular cofinality S-Space free Boolean algebra Reflecting stationary set transformations Martin's Axiom Chang's conjecture Luzin set Forcing Square-Brackets Partition Relations O-space Microscopic Approach HOD nonmeager set Large Cardinals Knaster and friends Uniformization Precaliber Commutative projection system Filter reflection Souslin Tree Mandelbrot set Minimal Walks super-Souslin tree Constructible Universe regressive Souslin tree Fast club stationary reflection Club Guessing Almost countably chromatic Ramsey theory over partitions Prevalent singular cardinals Generalized descriptive set theory Selective Ultrafilter Distributive tree Universal Sequences reflection principles incompactness Sigma-Prikry Partition Relations Singular Density Analytic sets
Update January 2024: Added a section “Club guessing with diamonds”, where we address the case of omega-bounded ladder systems.
Submitted to Journal of Symbolic Logic, December 2023.
Accepted, May 2024.
Update July 2024: Corrected Footnote #1. It used to say “for every lambda” and now says “for class many lambda’s”.