|Title:||Representing conjunctive deductions by disjunctive deductions||Journal:||Review of Symbolic Logic||Volume:||10||Issue:||1||First page:||145||Last page:||157||Issue Date:||1-Mar-2017||Rank:||M21||ISSN:||1755-0203||DOI:||10.1017/S175502031600037X||Abstract:||
A skeleton of the category with finite coproducts freely generated by a single object has a subcategory isomorphic to a skeleton of the category with finite products freely generated by a countable set of objects. As a consequence, we obtain that has a subcategory equivalent with . 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.
|Publisher:||Cambridge University Press|
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