EPSILON THEOREMS IN INTERMEDIATE LOGICS

AbstractPositive logics are $\{ \wedge , \vee , \to \}$-fragments of intermediate logics. It is clear that the positive fragment of $Int$ is not structurally complete. We give a description of all hereditarily structurally complete positive logics, while the question whether there is a structurally complete positive logic which is not hereditarily structurally complete, remains open.

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On finite approximability of ?-intermediate logics

Studia Logica ◽

10.1007/bf00373493 ◽

1982 ◽

Vol 41 (1) ◽

pp. 67-73

Author(s):

Wies?aw Dziobiak

Keyword(s):

Intermediate Logics ◽

Finite Approximability

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Tsutomu Hosoi. On intermediate logics. Journal of the Faculty of Science, University of Tokyo, section I, vol. 14 (1967), pp. 293–312, and vol. 16 (1969), pp. 1–12.

Journal of Symbolic Logic ◽

10.2307/2270285 ◽

1971 ◽

Vol 36 (2) ◽

pp. 329-330

Author(s):

A. S. Troelstra

Keyword(s):

Intermediate Logics

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Admissibility and refutation: some characterisations of intermediate logics

Archive for Mathematical Logic ◽

10.1007/s00153-014-0388-5 ◽

2014 ◽

Vol 53 (7-8) ◽

pp. 779-808 ◽

Cited By ~ 3

Author(s):

Jeroen P. Goudsmit

Keyword(s):

Intermediate Logics

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UNIFICATION IN INTERMEDIATE LOGICS

Journal of Symbolic Logic ◽

10.1017/jsl.2015.5 ◽

2015 ◽

Vol 80 (3) ◽

pp. 713-729 ◽

Cited By ~ 1

Author(s):

ROSALIE IEMHOFF ◽

PAUL ROZIÈRE

Keyword(s):

Intermediate Logics ◽

Unification Type

AbstractThis paper contains a proof–theoretic account of unification in intermediate logics. It is shown that many existing results can be extended to fragments that at least contain implication and conjunction. For such fragments, the connection between valuations and most general unifiers is clarified, and it is shown how from the closure of a formula under the Visser rules a proof of the formula under a projective unifier can be obtained. This implies that in the logics considered, for the n-unification type to be finitary it suffices that the m-th Visser rule is admissible for a sufficiently large m. At the end of the paper it is shown how these results imply several well-known results from the literature.

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