Models of VTC^0 as exponential integer parts
We prove that (additive) ordered group reducts of nonstandard models of the bounded arithmetical theory ๐ต๐ณ๐ข^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 ๐ต๐ณ๐ข^0, we show that every countable model of ๐ต๐ณ๐ข^0 is an exponential integer part of a real-closed exponential field.
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