منابع مشابه
Definable Sets in Ordered Structures
This paper introduces and begins the study of a well-behaved class of linearly ordered structures, the ^-minimal structures. The definition of this class and the corresponding class of theories, the strongly ©-minimal theories, is made in analogy with the notions from stability theory of minimal structures and strongly minimal theories. Theorems 2.1 and 2.3, respectively, provide characterizati...
متن کاملDEFINABLE SETS IN ORDERED STRUCTURES. Ill
We show that any o-minimal structure has a strongly o-minimal theory. 0. Introduction. In this paper we prove that an arbitrary o-minimal structure M is strongly o-minimal. This was proved in [1] in the case when the ordering on M is dense. In §1 we show that for discrete M, o-minimal implies strongly o-minimal. This is, of course, a result on uniform finite bounds. The proof has some interesti...
متن کاملDefinable Sets in Ordered Structures. Ii
It is proved that any O-minimal structure M (in which the underlying order is dense) is strongly O-minimal (namely, every N elementarily equivalent to M is O-minimal). It is simultaneously proved that if M is 0minimal, then every definable set of n-tuples of M has finitely many "definably connected components." 0. Introduction. In this paper we study the structure of definable sets (of tuples) ...
متن کاملDefinable Sets in Ordered Structures . I
This paper introduces and begins the study of a well-behaved class of linearly ordered structures, the ^-minimal structures. The definition of this class and the corresponding class of theories, the strongly ©-minimal theories, is made in analogy with the notions from stability theory of minimal structures and strongly minimal theories. Theorems 2.1 and 2.3, respectively, provide characterizati...
متن کاملDefinable Sets in Ordered Structures by Anand Pillay and Charles Steinhorn
1. Introduction. We introduce the notion of an O-minimal theory of ordered structures, such a theory being one such that the definable subsets of its models are particularly simple. The theory of real closed fields will be an example. For T an O-minimal theory we prove that over every subset A of a model there is a prime model, which is unique up to A-isomorphism. We also prove in our model-the...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1988
ISSN: 0002-9947
DOI: 10.2307/2000920