Around logical perfection
Abstract
In this article we present and describe a notion of "logical perfection". We extract the notion of "perfection" from the contemporary logical concept of categoricity. Categoricity (in power) has become in the past half century a main driver of ideas in model theory, both mathematically (stability theory may be regarded as a way of approximating categoricity) and philosophically. In the past two decades, categoricity notions have started to overlap with more classical notions of robustness and smoothness. These have been crucial in various parts of mathematics since the nineteenth century. We postulate and present the category of logical perfection. We draw on various notions of perfection from mathematics of the 19th and 20th centuries and then trace the relation to the concept of categoricity in power as a logical notion of what a "mathematically perfect" structure is.
Keywords
Cite
@article{arxiv.1803.04909,
title = {Around logical perfection},
author = {John Alexander Cruz Morales and Andrés Villaveces and Boris Zilber},
journal= {arXiv preprint arXiv:1803.04909},
year = {2019}
}
Comments
Title has changed.Exposition has been improved and some explanations are added. The second author is added