Approximation by simple structures
Abstract
In her graduate thesis, Gwyneth Harrison-Shermoen developed an abstract framework for approximating structures of a given theory, which generalized the notion of smoothly approximable structures. At the time it was unclear how broadly the framework applied due to a lack of examples. In this paper we will show that with slight modification to the framework, several well-understood NSOP1 theories are in fact approximable by simple structures. We discuss certain structural properties of the limit structure that can be obtained from the approximation and introduce a notion of limit dimension as a candidate for recovering Kim-independence in the limit structure. We also provide some examples of structures that are not approximable by structures of finite Morley rank.
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BibTeX
@misc{ellmanaspnes2026approximation,
title = {{Approximation by simple structures}},
author = {Katie Ellman-Aspnes},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06797},
eprint = {2609.06797},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06797},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Approximation by simple structures
AU - Katie Ellman-Aspnes
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.06797
UR - https://arxiv.org/abs/2609.06797
AB - In her graduate thesis, Gwyneth Harrison-Shermoen developed an abstract framework for approximating structures of a given theory, which generalized the notion of smoothly approximable structures. At the time it was unclear how broadly the framework applied due to a lack of examples. In this paper we will show that with slight modification to the framework, several well-understood NSOP_1 theories are in fact approximable by simple structures. We discuss certain structural properties of the limit structure that can be obtained from the approximation and introduce a notion of limit dimension as a candidate for recovering Kim-independence in the limit structure. We also provide some examples of structures that are not approximable by structures of finite Morley rank.
ER -