Transreal Proof of the Existence of Universal Possible Worlds

We extend various standard results of topology so that they apply to transreal spaces and use these to develop various results in logic. We prove that there are infinitely many, universal, possible worlds which approximate all possible words arbitrarily closely via application of a single, linear operator. Specifically that the universal worlds are hypercyclic. We also give a criterion to distinguish classical and paraconsistent logics.