# Models of VTC^0 as exponential integer parts

We prove that (additive) ordered group reducts of nonstandard models of the bounded arithmetical theory π΅π³π’^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 π΅π³π’^0, we show that every countable model of π΅π³π’^0 is an exponential integer part of a real-closed exponential field.

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