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