Abstract
AbstractIn the present paper, we give a systematic study of the correspondence theory of generalized modal algebras and generalized modal spaces, in the spirit of [3, 6]. The special feature of the present paper is that in the proof of the (right-handed) topological Ackermann lemma, the admissible valuations are not the clopen valuations anymore, but values in the set \(\mathcal {D}_{\mathcal {K}}(X)\) which are only closed and satisfy additional properties, not necessarily open. This situation is significantly different from existing settings using Stone/Priestley-like dualities, where all admissible valuations are clopen valuations.Keywordsgeneralized modal algebrageneralized modal spaceduality theorycorrespondence theory
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