Quantified universes and ultraproducts
A quantified universe is a set M equipped with a Riesz space of real functions on Mn, for each n, and a second order operation . Metric structures 4, graded probability structures 9 and many other structures in analysis are examples of such universes. We define ultraproduct of quantified universes and study properties preserved by this construction. We then discuss logics defined on the basis of classes of quantified universes which are closed under this construction.
universe ultraproduct metric structure ultra-closed class daniell structure. (msc2010) 03c20 03c65 03c80 03c90