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