caa a22 4500 388038829 CHVBK 20180307125015.0 cr unu---uuuuu 161130e199812 xx s 000 0 eng 10.2307/2586661 doi S0022481200014365 pii (NATIONALLICENCE)cambridge-10.2307/2586661 Keisler H. Jerome Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA. E-mail: keisler@math.wisc.edu Quantifier elimination for neocompact sets [Elektronische Daten] [H. Jerome Keisler] We shall prove quantifier elimination theorems for neocompact formulas, which define neocompact sets and are built from atomic formulas using finite disjunctions, infinite conjunctions, existential quantifiers, and bounded universal quantifiers. The neocompact sets were first introduced to provide an easy alternative to nonstandard methods of proving existence theorems in probability theory, where they behave like compact sets. The quantifier elimination theorems in this paper can be applied in a general setting to show that the family of neocompact sets is countably compact. To provide the necessary setting we introduce the notion of a law structure. This notion was motivated by the probability law of a random variable. However, in this paper we discuss a variety of model theoretic examples of the notion in the light of our quantifier elimination results. Copyright © Association for Symbolic Logic 1998 elimination nationallicence quantifier nationallicence neocompact nationallicence The Journal of Symbolic Logic Cambridge University Press 63/4(1998-12), 1442-1472 0022-4812 63:4<1442 1998 63 JSL https://doi.org/10.2307/2586661 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.2307/2586661 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Keisler H. Jerome Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA. E-mail: keisler@math.wisc.edu NATIONALLICENCE 773 0- The Journal of Symbolic Logic Cambridge University Press 63/4(1998-12), 1442-1472 0022-4812 63:4<1442 1998 63 JSL CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge