实域的开集展开：可定义性与可解释性
Expansions of the real field by open sets: definability versus interpretability
摘要：
产生实数R的开集U，使得实数域的展开式（R，+，x，U）定义（R，+，x，N）的Borel同构，但不定义N。因此，（R，+，x，U）定义了射影层次的每一层中的集合，但并不定义所有的射影集合。这一结果阐述了各种方式，涉及几何测度论和工作的O-最小的扩展（R，+，x）。特别地，存在R的康托子集K，使得对于（R，+，x）的每个指数有界的o-极小展开M，R的每个可定义在（M，K）中的子集要么有内部要么是Hausdorff null。
英文摘要：
An open set U of the real numbers R is produced such that the expansion (R,+,x,U) of the real field by U defines a Borel isomorph of (R,+,x,N) but does not define N. It follows that (R,+,x,U) defines sets in every level of the projective hierarchy but does not define all projective sets. This result is elaborated in various ways that involve geometric measure theory and working over o-minimal expansions of (R,+,x). In particular, there is a Cantor subset K of R such that for every exponentially bounded o-minimal expansion M of (R,+,x), every subset of R definable in (M,K) either has interior or is Hausdorff null.
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