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REPRESENTING CONJUNCTIVE DEDUCTIONS BY DISJUNCTIVE DEDUCTIONS

Published online by Cambridge University Press:  25 October 2016

KOSTA DOŠEN  and
ZORAN PETRIĆ
KOSTA DOŠEN*
Affiliation:
Mathematical Institute SANU
ZORAN PETRIĆ*
Affiliation:
Mathematical Institute SANU
*
*MATHEMATICAL INSTITUTE SANU KNEZ MIHAILOVA 36, P.F. 367 11001 BELGRADE, SERBIA E-mail: kosta@mi.sanu.ac.rs
†MATHEMATICAL INSTITUTE SANU KNEZ MIHAILOVA 36, P.F. 367 11001 BELGRADE, SERBIA E-mail: zpetric@mi.sanu.ac.rs
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Abstract

A skeleton of the category with finite coproducts${\cal D}$ freely generated by a single object has a subcategory isomorphic to a skeleton of the category with finite products ${\cal C}$ freely generated by a countable set of objects. As a consequence, we obtain that ${\cal D}$ has a subcategory equivalent with ${\cal C}$. From a proof-theoretical point of view, this means that up to some identifications of formulae the deductions of pure conjunctive logic with a countable set of propositional letters can be represented by deductions in pure disjunctive logic with just one propositional letter. By taking opposite categories, one can replace coproduct by product, i.e., disjunction by conjunction, and the other way round, to obtain the dual results.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 10 , Issue 1 , March 2017 , pp. 145 - 157
Copyright
Copyright © Association for Symbolic Logic 2016 

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