David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Studia Logica 45 (1):35 - 38 (1986)
Important positive as well as negative results on interpolation property in fragments of the intuitionistic propositional logic (INT) were obtained by J. I. Zucker in . He proved that the interpolation theorem holds in purely implicational fragment of INT. He also gave an example of a fragment of INT for which interpolation fails. This fragment is determined by the constant falsum (), well known connectives: implication () and conjunction (), and by a ternary connective defined as follows: (p, q, r)= df (pq)(pr).Extending this result of J. I. Zucker, G. R. Renardel de Lavalette proved in  that there are continuously many fragments of INT without the interpolation property.
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