Definable quotients in locally o-minimal structures

2022/12/13 by Fujita, Masato, Kawakami, Tomohiro
#03C64 #54B15 #57S99 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2212.06401

Abstract

Let \mathcal F=(F, +. ⋅, <, 0, 1, …) be a definably complete locally o-minimal expansion of an ordered field. We demonstrate the existence of definable quotients of definable sets by definable equivalence relations when several technical conditions are satisfied. These conditions are satisfied when X is a locally closed definable subset of Fⁿ and there is a definable proper action of a definable group G on X.

Related

• Definable quotients in d-minimal structures
• Definable groups as homomorphic images of semilinear and field-definable\n groups
• Approximation and zero set of definable functions in a definably complete locally o-minimal structure
• Groups and rings definable in d-minimal structures
• On the o-minimal LS-category