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