Abstract:
Fraenkel-Mostowski set theory represents an alternative set theory with
multiple applications in mathematics and computer science. It deals with
`finitely supported sets' instead of `sets'. The notions of `finite' and
`Dedekind finite' are different in this framework. Our main purpose is to
provide a complete characterization of Dedekind finite and Dedekind
infinite sets in Fraenkel-Mostowski set theory, and to study each class of
Dedekind finite and Dedekind infinite sets in an hierarchically defined
model of the Fraenkel-Mostowski set theory.
Key Words: Fraenkel-Mostowski set theory,
Dedekind finiteness, invariant set
2010 Mathematics Subject Classification: Primary 03E10. Secondary 03E25, 03E30.
