Embedded o-minimal structures

Authors

Assaf Hasson, Alf Onshuus

Type: Article

Publication Date: 2009-12-25

Citations: 10

DOI: https://doi.org/10.1112/blms/bdp098

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Abstract

We prove the following two theorems on embedded o-minimal structures: Theorem 1. Let ℳ ≺ 풩 be o-minimal structures and let ℳ* be the expansion of ℳ by all traces in M of 1-variable formulas in 풩, that is all sets of the form φ(M, ā) for ā ⊆ N and φ(x, ȳ) ∈ ℒ(풩). Then, for any N-formula ψ(x1, …, xk), the set ψ(Mk) is ℳ*-definable. Theorem 2. Let 풩 be an ω1-saturated structure and let S be a sort in 풩eq. Let 풮 be the 풩-induced structure on S and assume that 풮 is o-minimal. Then 풮 is stably embedded.

Locations

Bulletin of the London Mathematical Society
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Anand Pillay

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Anand Pillay

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Tomohiro Kawakami , Wakayama Univiversity

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Alfred Dolich , Chris Miller , Charles Steinhorn

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Assaf Hasson , Alf Onshuus

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Anand Pillay

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