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Definable Categorical Equivalence

Hudetz, Laurenz (2018) Definable Categorical Equivalence. [Preprint]


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This paper aims to provide a new criterion of formal equivalence of theories that is suitable for being supplemented with preservation conditions concerning interpretation. I argue that both the internal structure of models and choices of morphisms between models are aspects of formalisms that are relevant when it comes to their interpretations. So an adequate criterion should take these aspects into account. The two most important criteria presently discussed in philosophy of science---generalised definitional equivalence (Morita equivalence) and categorical equivalence---are not optimal in this respect. Generalised definitional equivalence neglects choices of morphisms, whereas categorical equivalence neglects the internal structure of models. I put forward the new criterion of definable categorical equivalence which takes into account both aspects and connects the category-theoretic approach and the definability-theoretic approach to formal equivalence.

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Item Type: Preprint
Keywords: Equivalence; scientific theories; models; categories; morphisms; definitions; translations
Subjects: Specific Sciences > Mathematics > Logic
General Issues > Structure of Theories
Depositing User: Mr. Laurenz Hudetz
Date Deposited: 16 Jan 2018 19:22
Last Modified: 16 Jan 2018 19:22
Item ID: 14297
Subjects: Specific Sciences > Mathematics > Logic
General Issues > Structure of Theories
Date: 16 January 2018

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