Saeed Salehi is a logician at the University of Tabriz in Iran. Three years ago he gave a presentation at a Moscow workshop on proofs of the diagonal lemma.
Today I thought I would discuss the famous diagonal lemma.
The lemma is related to Georg Cantor’s famous diagonal argument yet is different. The logical version imposes requirements on when the argument applies, and requires that it be expressible within a formal system.
The lemma underpins Kurt Gödel’s famous 1931 proof that arithmetic is incomplete. However, Gödel did not state it as a lemma or proposition or theorem or anything else. Instead, he focused his attention on what we now call Gödel numbering. We consider this today as «obvious» but his paper’s title ended with «Part I». And he had readied a «Part II» with over 100 pages of calculations should people question that his numbering scheme was expressible within…
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