Axiomatic Characterizations of Hyperuniverses and Applicationsa
Marco Forti, Furio Honsell, Marina Lenisa · Annals of the New York Academy of Sciences · 1996
ABSTRACT: Hyperuniverses are topological structures exhibiting strong closure properties under formation of subsets. They have been used both in computer science, for giving denotational semantics à la Scott‐de Bakker, and in mathematical logic, in order to show the consistency of set theories that do not abid***e by the “limitation‐of‐size” principle. We present correspondence between set‐theoretic properties and topological properties of hyperuniverses. We give existence theorems and discuss applications and generalizations to the non‐κ‐compact case.