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