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- W959662634 abstract "The study of extensions of first order predicate calculus lacks a program or an ideology. Such an ideology is usually provided by—patterns of possible theorems; hard open problems and hard theorems; and applications to other fields of mathematics or other sciences. For first order predicate calculus, the first and second aspect overlap: completeness and compactness theorem, Löwenheim and Hanf number calculations, categoricity theorems and definability theory give a good frame, and applications in algebra and non-standard analysis are well known. For extensions of predicate calculus a first try is to mimic classical model theory. Fewer hard theorems exist and hard open problems are scattered without much coherence. This chapter reviews results on countably compact extensions of Lѡѡ which have grown out of joint work with S. Shelah and J. Stavi. The chapter surveys the model theory of Lpww and Lww(aa) ,as far as they are parallel and exhibits their known differences and presents a modest application to topology." @default.
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- W959662634 date "1978-01-01" @default.
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- W959662634 title "Quantifying Over Countable Sets: Positive vs Stationary Logic" @default.
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- W959662634 doi "https://doi.org/10.1016/s0049-237x(08)72001-9" @default.
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