Mathematical Logic Quarterly 51 (3):254-257 (2005)

In [3] a certain family of topological spaces was introduced on ultraproducts. These spaces have been called ultratopologies and their definition was motivated by model theory of higher order logics. Ultratopologies provide a natural extra topological structure for ultraproducts. Using this extra structure in [3] some preservation and characterization theorems were obtained for higher order logics. The purely topological properties of ultratopologies seem interesting on their own right. We started to study these properties in [2], where some questions remained open. Here we present the solutions of two such problems. More concretely we show 1. that there are sequences of finite sets of pairwise different cardinalities such that in their certain ultraproducts there are homeomorphic ultratopologies and 2. if A is an infinite ultraproduct of finite sets, then every ultratopology on A contains a dense subset D such that |D| < |A|
Keywords ultratopology  Ultraproduct  dense set
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DOI 10.1002/malq.200410024
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Ultratopologies.Gábor Sági & János Gerlits - 2004 - Mathematical Logic Quarterly 50 (6):603-612.
Ultraproducts and Higher Order Formulas.Gábor Sági - 2002 - Mathematical Logic Quarterly 48 (2):261-275.

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Upward Morley's Theorem Downward.Gábor Sági & Zalán Gyenis - 2013 - Mathematical Logic Quarterly 59 (4-5):303-331.

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