Kant, Deborah (2023) The hidden use of new axioms. [Preprint]

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Abstract

This paper analyses the hidden use of new axioms in set-theoretic practice with a focus on large cardinal axioms and presents a general overview of set-theoretic practices using large cardinal axioms. The hidden use of a new axiom provides extrinsic reasons in support of this axiom via the idea of verifiable consequences, which is especially relevant for set-theoretic practitioners with an absolutist view. Besides that, the hidden use has pragmatic significance for further important sub-groups of the set-theoretic community---set-theoretic practitioners with a pluralist view and set-theoretic practitioners who aim for ZFC-proofs. By describing this, the paper gives a more complete picture of new axioms in set-theoretic practice. These observations, for instance, show that set-theoretic practitioners interested in ZFC-proofs use tools that go beyond ZFC. The analysis is based on empirical data that was
collected in an extensive interview study with set-theoretic practitioners.

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Item Type:	Preprint
Creators:	Creators Email ORCID Kant, Deborah kantdebo@gmail.com 0000-0002-5716-0924
Keywords:	Set-theoretic practice Large cardinal axioms
Subjects:	Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics General Issues > Social Epistemology of Science
Depositing User:	Deborah Kant
Date Deposited:	21 Dec 2023 17:36
Last Modified:	21 Dec 2023 17:36
Item ID:	22889
Subjects:	Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics General Issues > Social Epistemology of Science
Date:	25 November 2023
URI:	https://philsci-archive.pitt.edu/id/eprint/22889

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