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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

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

# 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