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Ulam matrix very good scale Souslin Tree Cardinal Invariants Sierpinski's onto mapping principle C-sequence Analytic sets transformations Fodor-type reflection Aronszajn tree P-Ideal Dichotomy Sigma-Prikry nonmeager set coloring number reflection principles Partition Relations 54G20 Sakurai's Bell inequality Axiom R Square-Brackets Partition Relations PFA square principles specializable Souslin tree Kurepa Hypothesis stick Hedetniemi's conjecture weak diamond Chang's conjecture Slim tree Fast club HOD Reflecting stationary set Hindman's Theorem Constructible Universe Cohen real Whitehead Problem L-space Almost-disjoint family free Souslin tree Hereditarily Lindelöf space club_AD Diamond-sharp Postprocessing function middle diamond Uniformly homogeneous Generalized descriptive set theory full tree Singular Density Martin's Axiom Cardinal function Was Ulam right ccc Luzin set Jonsson cardinal Rainbow sets indecomposable ultrafilter Erdos-Hajnal graphs GMA Dowker space Small forcing Prikry-type forcing SNR weak Kurepa tree polarized partition relation incompactness Parameterized proxy principle Successor of Singular Cardinal Singular cofinality Ramsey theory over partitions Vanishing levels Rado's conjecture Reduced Power Subnormal ideal countably metacompact Subadditive super-Souslin tree xbox Foundations diamond star Absoluteness Ascent Path Erdos Cardinal Rock n' Roll Chromatic number unbounded function Singular cardinals combinatorics Forcing AIM forcing Local Club Condensation. Uniformly coherent strongly bounded groups Dushnik-Miller Forcing Axioms stationary hitting Minimal Walks Greatly Mahlo sap Subtle cardinal Strongly Luzin set Nonspecial tree tensor product graph Closed coloring free Boolean algebra Prevalent singular cardinals Commutative cancellative semigroups Ostaszewski square approachability ideal Well-behaved magma regressive Souslin tree projective Boolean algebra Subtle tree property b-scale Non-saturation PFA(S)[S] Lipschitz reduction Fat stationary set Diamond for trees Universal Sequences Open Access Generalized Clubs Knaster Distributive tree Large Cardinals positive partition relation ZFC construction Shelah's Strong Hypothesis Amenable C-sequence Weakly compact cardinal weak square Selective Ultrafilter OCA O-space Uniformization Iterated forcing Successor of Regular Cardinal Mandelbrot set Antichain Club Guessing Knaster and friends Coherent tree square Precaliber Diamond Microscopic Approach stationary reflection higher Baire space Poset Almost countably chromatic Filter reflection Ineffable cardinal Almost Souslin Strong coloring S-Space
Blog Archives
Many diamonds from just one
Recall Jensen’s diamond principle over a stationary subset $S$ of a regular uncountable cardinal $\kappa$: there exists a sequence $\langle A_\alpha\mid \alpha\in S \rangle$ such that $\{\alpha\in S\mid A\cap\alpha=A_\alpha\}$ is stationary for every $A\subseteq\kappa$. Equivalently, there exists a sequence $\langle … Continue reading
Variations on diamond
Jensen’s diamond principle has many equivalent forms. The translation between these forms is often straight-forward, but there is one form whose equivalence to the usual form is somewhat surprising, and Devlin’s translation from one to the other, seems a little … Continue reading
c.c.c. forcing without combinatorics
In this post, we shall discuss a short paper by Alan Mekler from 1984, concerning a non-combinatorial verification of the c.c.c. property for forcing notions. Recall that a notion of forcing $\mathbb P$ is said to satisfy the c.c.c. iff … Continue reading
