Incompleteness Results in Kripke Bundle Semantics
Kazuaki Nagaoka, Eiko Isoda · Mathematical logic quarterly · 1997
Abstract Kripke bundle and C‐set semantics are known as semantics which generalize standard Kripke semantics. In [4] and in [1, 2] it is shown that Kripke bundle and C‐set semantics are stronger than standard Kripke semantics. Also it is true that C‐set semantics for superintuitionistic logics is stronger than Kripke bundle semantics ([6]). Modal predicate logic Q‐S4.1 is not Kripke bundle complete ([3] ‐ it is also yielded as a corollary to Theorem 6.1(a) of the present paper). This is shown by using difference of Kripke bundle semantics and C‐set semantics. In this paper, by using the same idea we show that incompleteness results in Kripke bundle semantics which are extended versions of [2].