For sequential theories, bi-interpretability via one-dimensional identity-preserving interpretations implies synonymy, proved with a weak Schröder-Bernstein theorem; an example shows the hypotheses are optimal.
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When Bi-interpretability implies Synonymy
For sequential theories, bi-interpretability via one-dimensional identity-preserving interpretations implies synonymy, proved with a weak Schröder-Bernstein theorem; an example shows the hypotheses are optimal.