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