Слабая транзитивность - реституция.
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Аннотация
The purpose of this paper is a restitution of a longstanding notion of weak-transitivity and a modal system, which may be identified with the set of formulas valid in all weak-transitive Kripke models. The modal system has a finite models property and can be axiomatized quite simple: it is the smolest normal logic to contain all instances of the formula $p\& \square p\rightarrow\square\square p$. The modal system is an especially interesting as the logic of all topological spaces provided that the limit-operation, a fundamental topological notion, is treated as the diamond modality.
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Эсакиа Л. Слабая транзитивность - реституция. // Логические исследования / Logical Investigations. 2001. Т. 8. C. 244-255.
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Литература
Church А. . Joum. Symb.Logic. 25 (1960), 263-264
Segerberg К. Decidability of S4.1, Theoria, 34 (1968), 7-20
MacKinsey J., Tarski A., The algebra of topology. Annals of Math. 45 (1944) 141-191
Aull C .E , Thron W.J. , Separaction axioms between T0 and Ti, Indag.Math. 24 (1962) 26-37
Segerberg К., ’’Somewhere else” and “some other time”, In: Wright and Wrong: mini-essay in honor of G.H.von Wright, Publ. the group in logic and methodology of Real Finland, 1976, 61-64.
Halmos P.,. Algebraic logic. Monadic Boolean algebras., Composit. math., 12 (1955) 217-249
Scroggs S.J., Extensions of the Lewis S5, Joum. Symb .Logic, 16 (1951) 112-120
de Rijke M., The Modal logic of inequality, Joum. Symb. Logic, 57 (19920 566-587
Esakia L. The Modal Logic of Topological spaces, The Georgian Acad.Sci., Preprint, 1976 (in Russian)
Segerberg К. Decidability of S4.1, Theoria, 34 (1968), 7-20
MacKinsey J., Tarski A., The algebra of topology. Annals of Math. 45 (1944) 141-191
Aull C .E , Thron W.J. , Separaction axioms between T0 and Ti, Indag.Math. 24 (1962) 26-37
Segerberg К., ’’Somewhere else” and “some other time”, In: Wright and Wrong: mini-essay in honor of G.H.von Wright, Publ. the group in logic and methodology of Real Finland, 1976, 61-64.
Halmos P.,. Algebraic logic. Monadic Boolean algebras., Composit. math., 12 (1955) 217-249
Scroggs S.J., Extensions of the Lewis S5, Joum. Symb .Logic, 16 (1951) 112-120
de Rijke M., The Modal logic of inequality, Joum. Symb. Logic, 57 (19920 566-587
Esakia L. The Modal Logic of Topological spaces, The Georgian Acad.Sci., Preprint, 1976 (in Russian)