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