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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
\|	\|	billwadge.com The complete story of Gödel incompleteness. [4100 views] \| Bill Wadge's Blog	4.3 parsecs away Travel
\|	\|	The famous mathematician Kurt Gödel proved two "incompleteness" theorems. This is their story. By the 1930s logicians, especially Tarski, had figured out the semantics of predicate logic. Tarski described what exactly was an 'interpretation' and what it meant for a formula to be true in an interpretation. Briefly, an interpretation is a nonempty set (the...	4.3 parsecs away Travel
\|	\|	xvw.lol xvw.lol - OCaml, modules, and import schemes	30.3 parsecs away Travel
\|		Using the module system open and include statements to reproduce common import patterns from other languages	30.3 parsecs away Travel