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- W2061060701 abstract "Much effort has been spent to prove that the reduced product operation preserves, and sometimes even strengthens the L -equivalence of structures, where L is some infinitary language. A similar result is suggested by the following well-known fact: Assume D is a nonprincipal ultrafilter on ω and, for n Є ω , C n is a set. If the ultra-product Π ω C n / D is infinite, it has a cardinality ≥ Hence, by Łos' theorem, (i) if and φ ( x ) is a first-order formula, then iff where Q is the unary quantifier “there are many.” We shall prove some generalizations of (i). In particular, we show (ii) if D is a nonprincipal ultrafilter over I = ω, and then where L(Q) is the language obtained from the first-order language by adding the quantifier Q . (ii) remains true, if D is an ω-regular or an atomless filter over a set I . Lipner [7] proved that if is regular, then the L(Q) -equivalence is preserved under direct products. We show that the assumption “ is regular” is necessary." @default.
- W2061060701 created "2016-06-24" @default.
- W2061060701 creator A5057233368 @default.
- W2061060701 date "1975-09-01" @default.
- W2061060701 modified "2023-09-27" @default.
- W2061060701 title "L(Q)-preservation theorems " @default.
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- W2061060701 doi "https://doi.org/10.2307/2272165" @default.
- W2061060701 hasPublicationYear "1975" @default.
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