Domain Extension and Ideal Elements in Mathematics†

Philosophia Mathematica 29 (3):366-391 (2021)
  Copy   BIBTEX

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.

Similar books and articles

Domain Extension and the Philosophy of Mathematics.Kenneth Manders - 1989 - Journal of Philosophy 86 (10):553-562.
Zermelo's Analysis of 'General Proposition'.R. Gregory Taylor - 2009 - History and Philosophy of Logic 30 (2):141-155.
Ideal Elements in Hilbert's Geometry.John Stillwell - 2014 - Perspectives on Science 22 (1):35-55.
What Numbers Are Real?Kenneth L. Manders - 1986 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1986:253 - 269.
Word extension: A key to early word learning and domain-specificity.Sandra R. Waxman - 2001 - Behavioral and Brain Sciences 24 (6):1121-1122.
The Nonstationary Ideal in the Pmax Extension.Paul B. Larson - 2007 - Journal of Symbolic Logic 72 (1):138 - 158.
Memes, minds and evolution.David Holdcroft & Harry Lewis - 2000 - Philosophy 75 (2):161-182.
Une correspondance entre anneaux partiels et groupes.Patrick Simonetta - 1997 - Journal of Symbolic Logic 62 (1):60-78.
Int-Soft Ideals of Pseudo MV-Algebras.Young Bae Jun, Seok-Zun Song & Hashem Bordbar - 2018 - Bulletin of the Section of Logic 47 (1):1-14.
Quotients of Boolean algebras and regular subalgebras.B. Balcar & T. Pazák - 2010 - Archive for Mathematical Logic 49 (3):329-342.

Analytics

Added to PP
2021-08-10

Downloads
229 (#80,738)

6 months
106 (#31,727)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Anna Bellomo
University of Vienna