@article{bellomo_domain_2021,
	title = {Domain {Extension} and {Ideal} {Elements} in {Mathematics}†},
	volume = {29},
	issn = {1744-6406},
	url = {https://doi.org/10.1093/philmat/nkab018},
	doi = {10.1093/philmat/nkab018},
	abstract = {Domain extension in mathematics occurs whenever a given mathematical domain is augmented so as to include new elements. Manders argues that the advantages of important cases of domain extension are captured by the model-theoretic notions of existential closure and model completion. In the specific case of domain extension via ideal elements, I argue, Manders’s proposed explanation does not suffice. I then develop and formalize a different approach to domain extension based on Dedekind’s Habilitationsrede, to which Manders’s account is compared. I conclude with an examination of three possible stances towards extensions via ideal elements.},
	number = {3},
	urldate = {2023-05-24},
	journal = {Philosophia Mathematica},
	author = {Bellomo, Anna},
	month = oct,
	year = {2021},
	pages = {366--391},
}

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