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Amenable C-sequence L-space Singular Density Jonsson cardinal reflection principles Partition Relations Hindman's Theorem Closed coloring Forcing middle diamond Cardinal function Ineffable cardinal Small forcing Greatly Mahlo b-scale Erdos-Hajnal graphs Mandelbrot set Kurepa Hypothesis Subtle cardinal Generalized Clubs Vanishing levels Ulam matrix Subadditive Singular cofinality full tree Local Club Condensation. Filter reflection diamond star Chromatic number Poset Large Cardinals 54G20 stick weak Kurepa tree Dowker space Club Guessing Ascent Path Rado's conjecture Reduced Power Martin's Axiom xbox countably metacompact Almost countably chromatic Generalized descriptive set theory Aronszajn tree ZFC construction weak diamond indecomposable ultrafilter Reflecting stationary set polarized partition relation Commutative cancellative semigroups specializable Souslin tree Dushnik-Miller sap Iterated forcing Prikry-type forcing projective Boolean algebra PFA Shelah's Strong Hypothesis tensor product graph Analytic sets Cardinal Invariants Successor of Singular Cardinal Uniformly homogeneous Almost Souslin Was Ulam right GMA super-Souslin tree S-Space Hedetniemi's conjecture Diamond Knaster and friends Singular cardinals combinatorics Forcing Axioms Fodor-type reflection Non-saturation free Boolean algebra very good scale Ramsey theory over partitions Selective Ultrafilter Axiom R Minimal Walks Subtle tree property Souslin Tree positive partition relation Uniformization nonmeager set Parameterized proxy principle stationary hitting Luzin set Prevalent singular cardinals Weakly compact cardinal Universal Sequences Precaliber higher Baire space weak square Well-behaved magma AIM forcing ccc Whitehead Problem Fat stationary set Erdos Cardinal club_AD Slim tree Rock n' Roll Strong coloring Ostaszewski square Coherent tree free Souslin tree transformations Hereditarily Lindelöf space square Successor of Regular Cardinal Rainbow sets stationary reflection Lipschitz reduction Fast club square principles Microscopic Approach Foundations HOD Chang's conjecture O-space Almost-disjoint family approachability ideal unbounded function Postprocessing function Sakurai's Bell inequality Knaster Constructible Universe Diamond-sharp P-Ideal Dichotomy Antichain Uniformly coherent C-sequence Cohen real OCA Nonspecial tree regressive Souslin tree SNR Open Access Subnormal ideal Sierpinski's onto mapping principle Distributive tree Strongly Luzin set strongly bounded groups Square-Brackets Partition Relations coloring number Diamond for trees Sigma-Prikry PFA(S)[S] incompactness Absoluteness
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The order-type of clubs in a square sequence
Recall Jensen’s notion of square: Definition (Jensen): For an infinite cardinal $\lambda$, $\square_\lambda$ asserts the existence of a sequence $\overrightarrow C=\left\langle C_\alpha\mid\alpha\in\text{acc}(\lambda^+)\right\rangle$ such that for every limit $\alpha<\lambda^+$: $C_\alpha$ is a club subset of $\alpha$ of order-type $\le\lambda$; if $\beta\in\text{acc}(C_\alpha)$, … Continue reading
Shelah’s solution to Whitehead’s problem
Whitehead problem notes in hebrew : Table of contents Chapter 0 Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 References
