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You are here		rjlipton.com Proving Peano Arithmetic Partially Consistent? \| Gödel's Lost Letter and P=NP
\|	\|	xorshammer.com What Happens When You Iterate Gödel's Theorem? - XOR's Hammer	3.6 parsecs away Travel
\|	\|	Let $latex \mathrm{PA}$ be Peano Arithmetic. Gödel's Second Incompleteness Theorem says that no consistent theory $latex T$ extending $latex \mathrm{PA}$ can prove its own consistency. (I'll write $latex \mathrm{Con}(T)$ for the statement asserting $latex T$'s consistency; more on this later.) In particular, $latex \mathrm{PA} + \mathrm{Con}(\mathrm{PA})$ is stronger than $latex \mathrm{PA}$. But certainly, given that...	3.6 parsecs away Travel
\|	\|	unstableontology.com Understanding Gödel's completeness theorem - Unstable Ontology	4.9 parsecs away Travel
\|	\|	(note: some readers may find the LaTeX more readable on LessWrong.) In this post I prove a variant of Gödel's completeness theorem. My intention has been to really understand the theorem, so that I am not simply shuffling symbols around, but am actually understanding why it is true. I hope it is helpful for at...	4.9 parsecs away Travel
\|	\|	jdh.hamkins.org Every function can be computable! \| Joel David Hamkins	5.2 parsecs away Travel
\|	\|	I'd like to share a simple proof I've discovered recently of a surprising fact: there is a universal algorithm, capable of computing any given function! Wait, what? What on earth do I ...	5.2 parsecs away Travel
\|	\|	linsdoodles.wordpress.com Pull up a Seat - Week 10 \| Lins Doodles	20.6 parsecs away Travel
\|		For XingfuMama's Pull up a seat Photo Challenge	20.6 parsecs away Travel