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There are many books articles that look to explain Godel's Incompleteness Theorems for laymen. Does anyone know of some good material (free online is most appreciated) that attempts to do the same for Tarski's Undefinability Theorem? Thanks.

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The Wikipedia entry linked in the question in fact isn't bad, and has excellent references. Or you could try this piece which aims to "be accessible to anyone with some experience in first-order logic". And you won't understand Tarski's theorem if you don't have some minimal formal background knowledge. (After all, the theorem is a limitative result about what can't be done in a formalized theory satisfying certain minimum conditions -- so you do need to know what a formalized theory is!)

Introductory books on Gödel's incompleteness theorems usually have sections on Tarksi's theorem too. I'd particularly recommend Raymond Smullyan's wonderful Godel's Incompleteness Theorems because you get to Tarski very quickly (or my Gödel book, but the journey takes longer).

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