Ivonne Victoria Pallares-Vega
Abstract
Abstract The early controversies surrounding the axiom of choice are well known, as are the many results that followed concerning its (in)dependence from, and equivalence to, other mathematical propositions. This paper focuses not on the logical status of the axiom but rather on showing why it fails in certain categories.
A significance statement is not available in the OpenAlex record.
A contribution statement is not available in the OpenAlex record.
Method details are not available in the OpenAlex metadata.
Findings are not separately available in the OpenAlex metadata.
Limitations are not available in the OpenAlex metadata.
Application details are not available in the OpenAlex metadata.
Abstract The early controversies surrounding the axiom of choice are well known, as are the many results that followed concerning its (in)dependence from, and equivalence to, other mathematical propositions. This paper focuses not on the logical status of the axiom but rather on showing why it fails in certain categories.
Key concepts: Axiom of choice, Axiom independence, Constructive set theory, Zermelo–Fraenkel set theory, Urelement, Axiom, Equivalence (formal languages), Mathematical economics