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full tree Diamond Forcing with side conditions Erdos-Hajnal graphs Cardinal Invariants Mandelbrot set countably metacompact Analytic sets reflection principles Uniformly coherent Kurepa Hypothesis Foundations Cohen real Greatly Mahlo Erdos Cardinal Jonsson cardinal weak Kurepa tree Ramsey theory over partitions Filter reflection GMA stationary hitting positive partition relation diamond star Dowker space incompactness Local Club Condensation. Strong coloring approachability ideal Commutative cancellative semigroups Strongly compact cardinal Was Ulam right? Vanishing levels Constructible Universe Square-Brackets Partition Relations middle diamond Almost-disjoint family Fat stationary set stationary reflection Generalized Clubs Strongly Luzin set Well-behaved magma Coherent tree Diamond for trees Entangled linear order Ulam matrix Rock n' Roll AIM forcing strongly bounded groups Forcing Dushnik-Miller perfectly normal Countryman line 54G20 Subnormal ideal Closed coloring Rado's conjecture Intersection model Parameterized proxy principle Iterated forcing weak square Singular Density Amenable C-sequence Ascent Path Chang's conjecture P-Ideal Dichotomy Sierpinski's onto mapping principle Slim tree Souslin Tree weak diamond super-Souslin tree Hedetniemi's conjecture Subtle tree property Sigma-Prikry Shelah's Strong Hypothesis Ineffable cardinal S-Space square Cardinal function free Souslin tree club_AD Fodor-type reflection xbox Axiom R Small forcing Chromatic number Open Access very good scale Fast club Aronszajn tree Singular cofinality Hereditarily Lindelöf space SNR Universal Sequences Hindman's Theorem Nonspecial tree Reduced Power free Boolean algebra unbounded function Prikry-type forcing Subtle cardinal Sakurai's Bell inequality Prevalent singular cardinals Non-saturation Subadditive regressive Souslin tree Ascending path Diamond-sharp Microscopic Approach PFA(S)[S] Weakly compact cardinal Knaster and friends b-scale C-sequence tensor product graph Forcing Axioms Selective Ultrafilter Absoluteness Almost Souslin Respecting tree higher Baire space indecomposable filter Almost countably chromatic Ostaszewski square Uniformization Commutative projection system L-space nonmeager set Precaliber Reflecting stationary set square principles Large Cardinals specializable Souslin tree Partition relations for trees polarized partition relation Interval topology on trees transformations Minimal Walks Partition Relations ZFC construction Knaster Distributive tree ccc coloring number Successor of Regular Cardinal Lipschitz reduction Poset HOD OCA Singular cardinals combinatorics Luzin set Whitehead Problem Club Guessing Rainbow sets Martin's Axiom PFA Uniformly homogeneous sap Generalized descriptive set theory O-space stick Successor of Singular Cardinal Postprocessing function Antichain Monotonically far projective Boolean algebra
Tag Archives: Absoluteness
Mathematics Colloquium, Bar-Ilan University, November 2013
I gave a colloquium talk at Bar-Ilan University on November 10, 2013. Title: Forcing as a tool to prove theorems Abstract: Paul Cohen celebrated solution to Hilbert’s first problem showed that the Continuum Hypothesis is independent of the usual axioms of … Continue reading
A large cardinal in the constructible universe
In this post, we shall provide a proof of Silver’s theorem that the Erdos caridnal $\kappa(\omega)$ relativizes to Godel’s constructible universe. First, recall some definitions. Given a function $f:[\kappa]^{<\omega}\rightarrow \mu$, we say that $I\subseteq\kappa$ is a set of indiscernibles for … Continue reading
