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