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I","{\"openalex\":\"W2010757891\",\"doi\":\"10.1090/s0002-9947-1986-0833697-x\"}","2026-05-20T12:10:36.247098896","2026-05-20T12:10:38.181519898","doi","10.1090/s0002-9947-1986-0833697-x","arxivId","openalexId","W2010757891","abstractText","This paper introduces and begins the study of a well-behaved class of linearly ordered structures, the O \\mathcal {O} -minimal structures. The definition of this class and the corresponding class of theories, the strongly O \\mathcal {O} -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 characterizations of O \\mathcal {O} -minimal ordered groups and rings. Several other simple results are collected in § 3 \\S 3 . The primary tool in the analysis of O \\mathcal {O} -minimal structures is a strong analogue of \"forking symmetry,\" given by Theorem 4.2. This result states that any (parametrically) definable unary function in an O \\mathcal {O} -minimal structure is piecewise either constant or an order-preserving or reversing bijection of intervals. 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Anand Pillay 人物

Anand Pillay · 相关文章