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weak diamond Universal Sequences Ramsey theory over partitions xbox Subtle cardinal Uniformly coherent Hindman's Theorem Local Club Condensation. Cardinal function Chromatic number Forcing Axioms Ascent Path approachability ideal Generalized Clubs Uniformly homogeneous weak square free Boolean algebra Sigma-Prikry tensor product graph GMA Parameterized proxy principle indecomposable ultrafilter Jonsson cardinal Poset countably metacompact Amenable C-sequence Antichain Chang's conjecture Successor of Singular Cardinal Strong coloring Almost Souslin Fat stationary set ccc P-Ideal Dichotomy b-scale stationary hitting Whitehead Problem Diamond full tree Forcing Foundations Rado's conjecture projective Boolean algebra unbounded function positive partition relation nonmeager set Almost countably chromatic Dowker space Prikry-type forcing Prevalent singular cardinals PFA coloring number Mandelbrot set free Souslin tree Partition Relations Well-behaved magma Distributive tree Diamond-sharp Nonspecial tree Singular cofinality O-space stick Fodor-type reflection OCA Open Access Erdos Cardinal Slim tree Souslin Tree Axiom R Iterated forcing reflection principles Lipschitz reduction super-Souslin tree stationary reflection Subadditive SNR Uniformization 54G20 polarized partition relation Singular cardinals combinatorics square principles Successor of Regular Cardinal Hereditarily Lindelöf space middle diamond Ostaszewski square Rock n' Roll diamond star higher Baire space Selective Ultrafilter Diamond for trees Was Ulam right Non-saturation ZFC construction Microscopic Approach Closed coloring Subnormal ideal Rainbow sets Reflecting stationary set Subtle tree property Almost-disjoint family Small forcing Greatly Mahlo Generalized descriptive set theory Dushnik-Miller strongly bounded groups Kurepa Hypothesis Luzin set Singular Density Vanishing levels Large Cardinals Cohen real incompactness Sakurai's Bell inequality Reduced Power Martin's Axiom Fast club HOD C-sequence Sierpinski's onto mapping principle Coherent tree Square-Brackets Partition Relations club_AD PFA(S)[S] Commutative cancellative semigroups Weakly compact cardinal Cardinal Invariants specializable Souslin tree Erdos-Hajnal graphs Postprocessing function Club Guessing AIM forcing regressive Souslin tree S-Space Shelah's Strong Hypothesis Analytic sets Ulam matrix Absoluteness Filter reflection transformations Precaliber Minimal Walks L-space Aronszajn tree sap Knaster Hedetniemi's conjecture square very good scale Knaster and friends Strongly Luzin set Ineffable cardinal Constructible Universe
Tag Archives: PFA
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
PFA and the tree property at $\aleph_2$
Recall that a poset $\langle T,\le\rangle$ is said to be a $\lambda^+$-Aronszajn tree, if it isomorphic to a poset $(\mathcal T,\subseteq)$ of the form: $\emptyset\in \mathcal T\subseteq{}^{<\lambda^+}\lambda$; Write $\mathcal T_\alpha:=\{\sigma\in\mathcal T\mid \text{dom}(\sigma)=\alpha\}$; for all $\alpha<\lambda^+$, $\mathcal T_\alpha$ has size $\le\lambda$, … Continue reading