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