### Archives

### Recent blog posts

- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- Generalizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- Happy new jewish year! September 24, 2014
- Square principles April 19, 2014
- Partitioning the club guessing January 22, 2014

### Keywords

05A17 Aronszajn tree weak square Cohen real Singular cardinals combinatorics Almost countably chromatic Rainbow sets approachability ideal Fodor-type reflection Uniformly coherent Jonsson cardinal Constructible Universe HOD square weak diamond Stevo Todorcevic Prevalent singular cardinals Hereditarily Lindelöf space Hedetniemi's conjecture middle diamond Almost-disjoint famiy Universal Sequences Distributive tree Shelah's Strong Hypothesis square principles Souslin Tree Club Guessing Mandelbrot set Absoluteness Square-Brackets Partition Relations Singular coﬁnality Singular Density Forcing Axioms Selective Ultrafilter P-Ideal Dichotomy Poset Chromatic number Hindman's Theorem PFA(S)[S] Almost Souslin ccc stationary reflection Successor of Singular Cardinal Sakurai's Bell inequality Axiom R projective Boolean algebra 05D10 Rock n' Roll Slim tree Rado's conjecture 11P99 Chang's conjecture coloring number Non-saturation Cardinal function Parameterized proxy principle sap Kurepa Hypothesis Successor of Regular Cardinal L-space tensor product graph S-Space PFA OCA 20M14 Minimal Walks xbox Generalized Clubs Fast club Weakly compact cardinal Uniformization Postprocessing function incompactness Antichain Large Cardinals diamond star Ascent Path Knaster Reduced Power b-scale Fat stationary set very good scale Forcing Coherent tree Erdos-Hajnal graphs Nonspecial tree free Boolean algebra reflection principles polarized partition relation Dushnik-Miller Partition Relations Martin's Axiom Erdos Cardinal stationary hitting Small forcing Commutative cancellative semigroups Whitehead Problem Cardinal Invariants Foundations Prikry-type forcing Ostaszewski square Microscopic Approach Diamond

# 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