# DEFINABLE SETS IN ORDERED STRUCTURES. I

@article{Pillay1986DEFINABLESI,
title={DEFINABLE SETS IN ORDERED STRUCTURES. I},
author={Anand Pillay and Charles Steinhorn},
journal={Transactions of the American Mathematical Society},
year={1986},
volume={295},
pages={565-592}
}
• Published 1986
• Mathematics
• Transactions of the American Mathematical Society
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 dLminlmal 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 characterizations of 41-minimal ordered groups and rings. Several other simple results are collected in §3. The… Expand
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