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