Notes on Undecidability and Incompleteness
نویسنده
چکیده
Let Q be Robinson’s weak theory of arithmetic. We use recursiontheoretical methods to show that Q is essentially undecidable. Consequently, any recursively axiomatizable theory in which Q is interpretable is undecidable and incomplete. This is a strengthening of theorems of Gödel, Rosser and Tarski. We also present proofs of Gödel’s First and Second Incompleteness Theorems. In these proofs, the role of Q is perhaps a bit unusual. 1 Undecidable Theories This section is based on a talk which I gave on November 18, 2008 in the Penn State Logic Seminar. Sankha Basu took notes, and this section is essentially a polished version of those notes.
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