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Reference.org
Tennenbaum's theorem
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<p>Tennenbaum's theorem, named for <a href="/facts/Stanley_Tennenbaum/hs4AygB9">Stanley Tennenbaum</a> who presented the theorem in 1959, is a result in <a href="/facts/Mathematical_logic/SaI7Y3wN">mathematical logic</a> that states that no <a href="/facts/Countable_set/Wj4DmWPv">countable</a> <a href="/facts/Non-standard_model_of_arithmetic/e3EktWqv">nonstandard model</a> of <a href="/facts/First-order_logic/lcISqWIg">first-order</a> <a href="/facts/Peano_arithmetic/DhhDnNug">Peano arithmetic</a> (PA) can be recursive (Kaye 1991:153ff). </p>