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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

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

# 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