Beth definability, interpolation and language splitting

Rohit Parikh

pp. 211-221

in: Johan van Benthem, Theo A. Kuipers, Henk Visser (eds), Logic and philosophy of science in the footsteps of E. W. Beth, Synthese 179 (2), 2011.

Abstract

Both the Beth definability theorem and Craig’s lemma (interpolation theorem from now on) deal with the issue of the entanglement of one language L 1 with another language L 2, that is to say, information transfer—or the lack of such transfer—between the two languages. The notion of splitting we study below looks into this issue. We briefly relate our own results in this area as well as the results of other researchers like Kourousias and Makinson, and Peppas, Chopra and Foo. Section 3 does contain one apparently new theorem.