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