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Preservation of interpolation and generalized negative translations

Negative translations have been introduced to show the equi-consistency of intuitionistic and classical logics. Since then, they have been generalized and used in several different contexts. In this talk a technique, inspired in the negative translation mechanism, to prove that Craig interpolation holds in a deductive system is presented. This technique is used to show that Craig interpolation is preserved by the fibring of deductive systems under mild requirements. Other preservation by fibring results are presented concerning the extension interpolation property and the Maehara interpolation property. This talk reports on joint work with Walter Carnielli and Cristina Sernadas.
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