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