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### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# 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