Dense pairs of o-minimal structures

• Autorzy: Lou van den Dries
• Języki publikacji: EN

Abstrakty

EN

The structure of definable sets and maps in dense elementary pairs of o-minimal expansions of ordered abelian groups is described. It turns out that a certain notion of "small definable set" plays a special role in this description.

Kategorie tematyczne

• 06F20: Ordered abelian groups, Riesz groups, ordered linear spaces
• 03C60: Model-theoretic algebra
• 03C10: Quantifier elimination, model completeness and related topics
• 03C35: Categoricity and completeness of theories

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1998
• Tom: 157
• Numer: 1
• Strony: 61-78

Daty

wydano

1998

otrzymano

1997-07-24

poprawiono

1997-12-30

Twórcy

autor

Lou van den Dries

• Department of Mathematics, University of Illinois, Urbana, Illinois 61801, U.S.A.

Bibliografia

• [1] L. van den Dries and A. Lewenberg, T-convexity and tame extensions, J. Symbolic Logic 60 (1995), 74-102.
• [2] E. Hrushovski, Strongly minimal expansions of algebraically closed fields, Israel J. Math. 79 (1992), 129-151.
• [3] A. Macintyre, Dense embeddings I: a theorem of Robinson in a general setting, in: Model Theory and Algebra. A Memorial Tribute to Abraham Robinson; D. H. Saracino and V. B. Weispfenning (eds.), Lecture Notes in Math. 498, Springer, Berlin, 1975, 200-219.
• [4] H. D. MacPherson, D. Marker and C. Steinhorn, Weakly o-minimal theories and real closed fields, preprint.
• [5] C. Miller and P. Speissegger, Expansions of the real line by open sets: o-minimality and open cores, preprint.
• [6] Y. Peterzil and S. Starchenko, A trichotomy theorem for o-minimal structures, Proc. London Math. Soc., to appear.
• [7] A. Pillay and C. Steinhorn, Definable sets in ordered structures. I, Trans. Amer. Math. Soc. 295 (1986), 565-592.
• [8] A. Robinson, Solution of a problem of Tarski, Fund. Math. 47 (1959), 79-204.