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