WHEN BI-INTERPRETABILITY IMPLIES SYNONYMY
VISSER, ALBERT
Two salient notions of sameness of theories are synonymy , aka definitional equivalence , and bi-interpretability . Of these two definitional equivalence is the strictest notion. In which cases can we infer synonymy from bi-interpretability? We study this question for the case of sequential theories. Our result is as follows. Suppose that two sequential theories are bi-interpretable and that the interpretations involved in the bi-interpretation are one-dimensional and identity preserving. Then,