### 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

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

# 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