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Grothendieck Universes and Indefinite Extensibility

By Khudairi, Hasen

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Book Id: WPLBN0100003132
Format Type: PDF (eBook)
File Size: 160.09 KB
Reproduction Date: 9/2/2018

Title: Grothendieck Universes and Indefinite Extensibility  
Author: Khudairi, Hasen
Volume:
Language: English
Subject: Non Fiction, Philosophy
Collections: Authors Community, Philosophy
Historic
Publication Date:
2018
Publisher: Gutenberg
Member Page: Hasen Khudairi

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Khudairi, H. (2018). Grothendieck Universes and Indefinite Extensibility. Retrieved from http://www.self.gutenberg.org/


Description
This essay endeavors to define the concept of indefinite extensibility in the setting of category theory. I argue that the generative property of indefinite extensibility in the category-theoretic setting is identifiable with the Kripke functors of modal coalgebraic automata, where the automata model Grothendieck Universes and the functors are further inter-definable with the elementary embeddings of large cardinal axioms. The Kripke functors definable in Grothendieck universes are argued to account for the ontological expansion effected by the elementary embeddings in the category of sets. By characterizing the modal profile of $\Omega$-logical validity, and thus the generic invariance of mathematical truth, modal coalgebraic automata are further capable of capturing the notion of definiteness, in order to yield a non-circular definition of indefinite extensibility.


 

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