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