Absolutely independent axiomatizations for countable sets in classical logic
In (classical) propositional logic, a set A of sentences is called absolutely independent if for any ordered partition \(<A_ 1,A_ 2>\) of A, the set \(A_ 1\cup \{\neg p|\) \(p\in A_ 2\}\) is consistent. It is shown that a countable consistent set of sentences has always an absolutely independent axiomatization.
scientific article; zbMATH DE number 4123697