DEDUCTIVE CARDINALITY RESULTS AND NUISANCE-LIKE PRINCIPLES

• Published in: The review of symbolic logic Vol. 14; no. 3; pp. 592 - 623
• Main Author: EBELS-DUGGAN, SEAN C.
• Format: Journal Article
• Language: English
• Published: New York, USA Cambridge University Press 01.09.2021
• Subjects: Incompatibility; Logic; Mathematical analysis; Nuisance; Paradoxes; Principles; Russell, Bertrand Arthur William (1872-1970); Semantics; neo-logicism; 00A30; Cantor’s theorem; second-order logic; abstraction principles; cardinality; 03A05

The injective version of Cantor’s theorem appears in full second-order logic as the inconsistency of the abstraction principle, Frege’s Basic Law V (BLV), an inconsistency easily shown using Russell’s paradox. This incompatibility is akin to others—most notably that of a (Dedekind) infinite universe...