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

# 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