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Singular cardinals combinatorics Sakurai's Bell inequality Lipschitz reduction Poset Foundations Amenable C-sequence Almost countably chromatic Countryman line Microscopic Approach Coherent tree Chang's conjecture Club Guessing C-sequence SNR Absoluteness Subtle tree property Dushnik-Miller Strongly compact cardinal Ostaszewski square stick very good scale square principles nonmeager set Distributive tree Constructible Universe Souslin Tree Uniformization projective Boolean algebra free Boolean algebra Almost Souslin Successor of Regular Cardinal super-Souslin tree Ineffable cardinal Axiom R Closed coloring xbox PFA(S)[S] Martin's Axiom Analytic sets Luzin set Erdos Cardinal higher Baire space Greatly Mahlo Aronszajn tree Local Club Condensation. Successor of Singular Cardinal Parameterized proxy principle strongly bounded groups Universal Sequences Commutative cancellative semigroups PFA approachability ideal unbounded function Dowker space Commutative projection system Filter reflection Was Ulam right Diamond for trees Ulam matrix Open Access Forcing square Whitehead Problem Weakly compact cardinal positive partition relation S-Space Generalized Clubs indecomposable ultrafilter Intersection model Uniformly homogeneous Rock n' Roll free Souslin tree weak Kurepa tree Postprocessing function GMA Diamond-sharp ZFC construction Singular cofinality Hindman's Theorem Selective Ultrafilter Cardinal Invariants Fast club Knaster polarized partition relation Subnormal ideal weak square Square-Brackets Partition Relations middle diamond Vanishing levels OCA Chromatic number Uniformly coherent Kurepa Hypothesis stationary reflection Rado's conjecture sap coloring number Shelah's Strong Hypothesis AIM forcing full tree Jonsson cardinal Singular Density O-space Minimal Walks Prikry-type forcing Non-saturation Reflecting stationary set Subtle cardinal Erdos-Hajnal graphs Antichain club_AD Iterated forcing Precaliber diamond star Large Cardinals Small forcing Hereditarily Lindelöf space regressive Souslin tree Forcing Axioms incompactness Well-behaved magma Diamond Sigma-Prikry L-space Mandelbrot set Knaster and friends stationary hitting weak diamond Strong coloring b-scale Respecting tree Sierpinski's onto mapping principle HOD Partition Relations Slim tree Rainbow sets Ascent Path P-Ideal Dichotomy Nonspecial tree countably metacompact reflection principles Reduced Power specializable Souslin tree 54G20 Fodor-type reflection Strongly Luzin set Fat stationary set ccc Almost-disjoint family Prevalent singular cardinals Hedetniemi's conjecture Cohen real Ramsey theory over partitions Generalized descriptive set theory tensor product graph Subadditive Cardinal function transformations
Tag Archives: Large Cardinals
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
On the consistency strength of the Milner-Sauer conjecture
Abstract: In their paper from 1981, Milner and Sauer conjectured that for any poset $\mathbb P$, if $\text{cf}(\mathbb P)$ is a singular cardinal $\lambda$, then $\mathbb P$ must contain an antichain of size $\text{cf}(\lambda)$. The conjecture is consistent and known … Continue reading
