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1 Topological universes
3 Generalized positive comprehension
6 other sections not shown
accumulation point approximate the naive Approximation Principle arbitrary intersections assumption axiom axiom of choice axiom of foundation c.f. proof called Cauchy sequence central scale classical set CLASSIFICATION THEORY clopen closed sets closed under arbitrary comprehension scheme inside comprehension theoretic containing contradicts corresponding Define inductively Density Principle descending chain dual power sets easy to check elements empty set follows at once follows,we shall take formula Hence hereditarily homeomorphism implies inaccessible inside of classical large cardinals Maximal Union Principle Maximality Principle maximally compact universe minimal model of POS-COMP monotone naive comprehension scheme Now,we obviously octree perfect universe POS-U-COMP positive comprehension schemes power and dual product topologies proof of Th Prop quantifiers regular cardinal regular scale resp result S-COMP set extension set topology singleton Suppose tion point topological universe topological universe,then universal set theory universe iff urelements weakly compact wellfounded sets