Submission date: 10 May 2012.

Abstract:

We investigate real closed fields with an integer part that is a model of Peano Arithmetic (PA). We prove that such fields always allow left exponentiation. As a corollary, we obtain a large class of real closed fields without an integer part that is a model of PA. In particular, this includes uncountable, recursively saturated examples. This proves that the countability assumption in the recent theorem of P. D'Aquino, J. Knight and S. Starchenko is necessary.

Mathematics Subject Classification:

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Full text arXiv 1205.2254: pdf, ps.