Meadows, Toby (2024) The Halvorson Examples. [Preprint]

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Abstract

Halvorson has proposed an intriguing example of a pair of theories whose categories are equivalent but which are not themselves definitionally equivalent. Moreover, it seems obvious that these theories are not equivalent in any intuitive sense. We offer a new topological proof that these theories are not definitionally equivalent. However, the underlying theorem for this claim has a converse that shows a surprising collection of theories, which are superficially similar to those in Halvorson's example, turn out to be definitionally equivalent after all. This offers some new insight into what is going “wrong” in the Halvorson example.

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Item Type:	Preprint
Creators:	Creators Email ORCID Meadows, Toby meadowst@uci.edu
Keywords:	theoretical equivalence; category theory; intepretation
Subjects:	General Issues > Structure of Theories General Issues > Theory Change
Depositing User:	Dr Toby Meadows
Date Deposited:	13 Sep 2025 12:28
Last Modified:	13 Sep 2025 12:28
Item ID:	26635
Subjects:	General Issues > Structure of Theories General Issues > Theory Change
Date:	4 December 2024
URI:	https://philsci-archive.pitt.edu/id/eprint/26635

Available Versions of this Item

• The Halvorson Examples. (deposited 05 Dec 2024 13:06)
  • The Halvorson Examples. (deposited 13 Sep 2025 12:28) [Currently Displayed]

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