Mutual translatability, equivalence, and the structure of theories

Thomas William Barrett, Hans Halvorson

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


This paper presents a simple pair of first-order theories that are not definitionally (nor Morita) equivalent, yet are mutually conservatively translatable and mutually ‘surjectively’ translatable. We use these results to clarify the overall geography of standards of equivalence and to show that the structural commitments that theories make behave in a more subtle manner than has been recognized.

Original languageEnglish (US)
Article number240
Issue number3
StatePublished - Jun 2022

All Science Journal Classification (ASJC) codes

  • Philosophy
  • General Social Sciences


  • Cantor–Bernstein
  • Equivalence
  • Structure
  • Translation
  • co-Cantor–Bernstein


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