2024/12/10 by Babak Jabbar Nezhad, Nezhad, Babak Jabbar
Economics, Econometrics and Finance · #03E25 #03F55 #13P05 #30C15 #Economic theories and models #FOS: Mathematics #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.2412.08667
openalex publication_date 2024/12/10 · openalex created_date 2024/12/14 · openalex updated_date 2026/07/28
Bishop's constructive mathematics school rejects the Law of Excluded Middle, but instead vastly makes use of weaker versions of the Choice. In this paper we pioneer an example, which shows that this road is not consistent, as our example provides a paradox. Therefore, rejecting the Law of Excluded Middle, and as an alternative using the Countable Axiom of Choice and the Axiom of Dependent Choice, still does not create a consistent structure. Actually, constructively; the Countable Axiom of Choice is an implication of the Axiom of Dependent Choice.