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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

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

# 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