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