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