Two Main Results About Propositional Core Logic

The two main titular results are (I) no finite matrix of values characterizes propositional Core Logic C C , and (II) the connectives of propositional Core Logic are independent. These results echo the corresponding ones for propositional Intuitionistic Logic. Our reason for expounding them for Core Logic is that their metaproofs are easier and more accessible in that setting; and the result for Intuitionistic Logic corresponding to (II) is then a corollary to the Admissibility of Cut in Core Logic.