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