Quantified universes and ultraproducts

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Mathematical Logic Quarterly 58 (1-2):63-74 (2012)
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Abstract

A quantified universe is a set M equipped with a Riesz space equation image of real functions on Mn, for each n, and a second order operation equation image. 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.

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10.1002/malq.201190020

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The logic of integration.Seyed-Mohammad Bagheri & Massoud Pourmahdian - 2009 - Archive for Mathematical Logic 48 (5):465-492.
Probability logic.Douglas N. Hoover - 1978 - Annals of Mathematical Logic 14 (3):287.

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