Geodesic
Interpolation and the projective Beth property in well-composed logics
Algebra i logika, Tome 51 (2012) no. 2, pp. 244-275

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We study the interpolation and Beth definability problems in propositional extensions of minimal logic J. Previously, all J-logics with the weak interpolation property (WIP) were described, and it was proved that WIP is decidable over J. In this paper, we deal with so-called well-composed J-logics, i.e., J-logics satisfying the axiom $(\bot\to A)\vee(A\to\bot)$. Representation theorems are proved for well-composed logics possessing Craig's interpolation property (CIP) and the restricted interpolation property (IPR). As a consequence it is shown that only finitely many well-composed logics share these properties, and that IPR is equivalent to the projective Beth property (PBP) on the class of well-composed J-logics.
Keywords: well-composed J-logic, Beth definability.
Mots-clés : interpolation 
@article{AL_2012_51_2_a6,
     author = {L. L. Maksimova},
     title = {Interpolation and the projective {Beth} property in well-composed logics},
     journal = {Algebra i logika},
     pages = {244--275},
     publisher = {mathdoc},
     volume = {51},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2012_51_2_a6/}
}
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L. L. Maksimova. Interpolation and the projective Beth property in well-composed logics. Algebra i logika, Tome 51 (2012) no. 2, pp. 244-275. http://geodesic.mathdoc.fr/item/AL_2012_51_2_a6/