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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
- Genearlizations 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

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

# 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