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