Ultraproducts and Higher Order Formulas

Mathematical Logic Quarterly 48 (2):261-275 (2002)

Abstract
Which ultraproducts preserve the validity of formulas of higher order logics? To answer this question, we will introduce natural topologies on ultraproducts. We will show, that ultraproducts preserving certain higher order formulas can be characterized in terms of these topologies. As an application of the above results, we provide a constructive, purely model theoretic characterization for classes definable by second order existential formulas
Keywords higher order elementary class  higher order formula  ultraproduct  preservation
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DOI 10.1002/1521-3870(200202)48:2<261::AID-MALQ261>3.0.CO;2-F
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References found in this work BETA

Limit Ultraproducts.H. Jerome Keisler - 1965 - Journal of Symbolic Logic 30 (2):212-234.

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Citations of this work BETA

On Topological Properties of Ultraproducts of Finite Sets.Gábor Sági & Saharon Shelah - 2005 - Mathematical Logic Quarterly 51 (3):254-257.
Upward Morley's Theorem Downward.Gábor Sági & Zalán Gyenis - 2013 - Mathematical Logic Quarterly 59 (4-5):303-331.

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