Jump to ContentJump to Main Navigation
Philosophy and Model Theory$
Users without a subscription are not able to see the full content.

Tim Button and Sean Walsh

Print publication date: 2018

Print ISBN-13: 9780198790396

Published to Oxford Scholarship Online: May 2018

DOI: 10.1093/oso/9780198790396.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 28 October 2021

Classification and uncountable categoricity

Classification and uncountable categoricity

Chapter:
(p.413) 17 Classification and uncountable categoricity
Source:
Philosophy and Model Theory
Author(s):

Tim Button

Sean Walsh

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198790396.003.0017

The topic of this chapter is classification. We start by formulating a wholly general philosophical framework for understanding classification programs within mathematics, in which calculable invariants play an important role. We then consider the most famous classification program in contemporary model theory, due to Shelah, who has suggested that classification concerns identifying which theories do not have too many models. We critically compare these two different perspectives on classification— calculable mechanisms vs. not too many models. We close the chapter by discussing Zilber's ambitious proposal for the classification of uncountably categorical theories (i.e. theories which have only one model up to isomorphism in a given uncountable cardinality). Whereas categoricity was seen as a potential philosophical salve in chapters 6-8, Zilber's program regards uncountable categoricity as a kind of extreme classification.

Keywords:   Invariants, calculable mechanisms, Main Gap Theorem, Shelah’s classification programme, uncountably categorical, The Trichotomy Conjecture

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .