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NEIGHBOURHOOD CANONICITY FOR EK, ECK, AND RELATIVES: A CONSTRUCTIVE PROOF
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- Journal:
- The Review of Symbolic Logic / Volume 15 / Issue 3 / September 2022
- Published online by Cambridge University Press:
- 02 July 2021, pp. 607-623
- Print publication:
- September 2022
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- Article
- Export citation
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We prove neighbourhood canonicity and strong completeness for the logics
$\mathbf {EK}$
and 
$\mathbf {ECK}$
, obtained by adding axiom (K), resp. adding both (K) and (C), to the minimal modal logic 
$\textbf {E}$
. In contrast to an earlier proof in [10], ours is constructive. More precisely, we construct minimal characteristic models for both logics and do not rely on compactness of first order logic. The proof involves a specific circumscription technique and quite some set-theoretic maneuvers to establish that the models satisfy the appropriate frame conditions. After giving both proofs, we briefly spell out how they generalize to four stronger logics and to the extensions of the resulting six logics with a global modality.
