Models of $VT{C}^0$ as exponential integer parts

Abstract

We prove that (additive) ordered group reducts of nonstandard models of the bounded arithmetical theory $\mathsf{VT}{\mathsf{C}}^0$ 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 $\mathsf{VT}{\mathsf{C}}^0$, we show that every countable model of $\mathsf{VT}{\mathsf{C}}^0$ is an exponential integer part of a real-closed exponential field.

22 pages

References in corpus (2)

• Open induction in a bounded arithmetic for TC^0
• Elementary analytic functions in $VT{C}^0$

Cited by in corpus (1)

• Analogues of Shepherdson's Theorem for a language with exponentiation