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### 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

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