Submission date: 2 September 2022

Abstract:

We prove that (additive) ordered group reducts of nonstandard models of the bounded arithmetical theory VTC^0 are recursively saturated in a rich language with predicates expressing the integers, rationals, and logarithmically bounded numbers. Combined with our previous results on the construction of the real exponential function on completions of models of VTC^0, we show that every countable model of VTC^0 is an exponential integer part of a real-closed exponential field.

Mathematics Subject Classification: 03C62 (Primary) 03C64, 03C50, 03F20 (Secondary)

Keywords and phrases:

Full text arXiv 2209.01197: pdf, ps.