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Axiomatic Characterizations of Hyperuniverses and Applications a
Author(s) -
FORTI MARCO,
HONSELL FURIO,
LENISA MARINA
Publication year - 1996
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1996.tb49165.x
Subject(s) - closure (psychology) , consistency (knowledge bases) , denotational semantics , set (abstract data type) , axiom , set theory , semantics (computer science) , mathematics , axiomatic system , discrete mathematics , algebra over a field , pure mathematics , topology (electrical circuits) , computer science , combinatorics , programming language , operational semantics , geometry , economics , market economy
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.