Transreal Explicit Construction of Universal Possible Worlds

Abstract

In an earlier paper we supplied an indirect proof of the existence of universal possible worlds that have the topological property of being hypercyclic, which means they can access every world in sequences of worlds that approach arbitrarily closely to every possible world. That proof states that there are universal worlds but it does not exhibit such a world explicitly. We now explicitly construct two such universal worlds. A continuous universal world constructs possible worlds with transreal co-ordinates directly. A discrete world provides a binary hypercyclic vector which can be used to create transfloating-point co-ordinates that approximate transreal co-ordinates. We also discuss the philosophical implications of universal worlds for an omniscient observer and human science.