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arXiv · 2204.11973

On Automorphism Criteria for Comparing Amounts of Mathematical Structure

Thomas William Barrett·JB Manchak·James Owen Weatherall
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Abstract

Wilhelm (2021) has recently defended a criterion for comparing structure of mathematical objects, which he calls Subgroup. He argues that Subgroup is better than SYM * , another widely adopted criterion. We argue that this is mistaken; Subgroup is strictly worse than SYM *. We then formulate a new criterion that improves on both SYM * and Subgroup, answering Wilhelm's criticisms of SYM * along the way. We conclude by arguing that no criterion that looks only to the automorphisms of mathematical objects to compare their structure can be fully satisfactory.

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Thomas William Barrett, JB Manchak, James Owen Weatherall. 2022-04-25. On Automorphism Criteria for Comparing Amounts of Mathematical Structure. https://arxiv.org/abs/2204.11973

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