Geodesic
Dedekind Completeness and the Algebraic Complexity of o-Minimal Structures
Canadian journal of mathematics, Tome 44 (1992) no. 4, pp. 843-855

Voir la notice de l'article provenant de la source Cambridge University Press

An ordered structure is o-minimal if every definable subset is the union of finitely many points and open intervals. A theory is o-minimal if all its models are ominimal. All theories considered will be o-minimal. A theory is said to be n-ary if every formula is equivalent to a Boolean combination of formulas in n free variables. (A 2-ary theory is called binary.) We prove that if a theory is not binary then it is not rc-ary for any n. We also characterize the binary theories which have a Dedekind complete model and those whose underlying set order is dense. In [5], it is shown that if T is a binary theory, is a Dedekind complete model of T, and I is an interval in , then for all cardinals K there is a Dedekind complete elementary extension of , so that . In contrast, we show that if T is not binary and is a Dedekind complete model of T, then there is an interval I in so that if is a Dedekind complete elementary extension of .
DOI : 10.4153/CJM-1992-050-1
Mots-clés : Primary: 03C07, secondary: 03C65 
Mekler, Alan; Rubin, Matatyahu; Steinhorn, Charles. Dedekind Completeness and the Algebraic Complexity of o-Minimal Structures. Canadian journal of mathematics, Tome 44 (1992) no. 4, pp. 843-855. doi: 10.4153/CJM-1992-050-1
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