Models of VTC^0 as exponential integer parts

09/02/2022

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by   Emil Jeřábek, et al.

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Akademie věd ČR

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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.