Abstract
Abstract We will now start developing number theory in PA. One of our main goals is to prove a version of the Chinese remainder theorem. This will enable us to prove Godel’s lemma (Lemma 3.2) for arbitrary models of PA. As an application we will show how to derive Euclid’s theorem on the infinitude of the primes in PA. (This theorem, coincidentally, is the first ‘real’ mathematical theorem that Hardy proves in his Apology!) In fact, equipped with Godel’s lemma, the reader will see that it is routine to transcribe the proofs of many theorems in number theory into PA.
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