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HEREDITARILY STRUCTURALLY COMPLETE POSITIVE LOGICS

Published online by Cambridge University Press:  23 April 2019

ALEX CITKIN
ALEX CITKIN*
Affiliation:
Metropolitan Telecommunications
*
*INFORMATION TECHNOLOGY METROPOLITAN COMMUNICATIONS 55 WATER STREET, 32 FLOOR NEW YORK, NY 10041, USA E-mail: acitkin@gmail.com
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Abstract

Positive 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.

Keywords

03B5503B6003C05intermediate logicpositive logicprimitive varietyHeyting algebraimplicative lattice

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Type
Research Article
Information
The Review of Symbolic Logic , Volume 13 , Issue 3 , September 2020 , pp. 483 - 502
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Copyright
Copyright © Association for Symbolic Logic 2019 

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