Two basic results on translations between logics
Edward Hermann Hæusler, Luiz Carlos Pereira · DOAJ (DOAJ: Directory of Open Access Journals) · 2016
The aim of the present paper is to show two basic results concerning translation between logics: [1] The first result establishes that given two logics S1 and S2 with languages L1 and L2, and a translation F of L1 into L2 that interprets S1 into S2, then, given any intermediate logic S3 between S1 and S2, the same translation F interprets S1 into S3. [2] The second result establishes that the translation F cannot interpret S3 into S2.