Structure theorem for i-minimal expansions of the real additive ordered group

2020/04/30 by Savatovsky, Alex
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2005.00063

Abstract

We prove that for an o-minimal expansion of the real additive group \cal R and a set P⊆ ℝ of dimension 0 such that \langleR,P⟩ is sparse, has definable choice and every definable set has interior or is nowhere dense then, for every definable set X, there is a family \X_t: t∈ A\ definable in \Cal R and a set S⊆ A of dimension 0 such that X=\bigcup_{t∈ S}X_t. Moreover, in the d-minimal setting, there is a finite decomposition of X into sets of the previous form such that for every t∈ S X_t is relatively open in \bigcup_{t∈ S}X_t.

Related

• Connected components in d-minimal structures
• Sparse regular subsets of the reals
• Externally definable quotients and NIP expansions of the real ordered\n additive group
• A tetrachotomy for expansions of the real ordered additive group
• Structure theorems in tame expansions of o-minimal structures by a dense set