the empty set is not taken as a part of this system (since it can be derived from ZF + Infinity), then the empty domain also satisfies ZFC – Infinity + ¬Infinity, as all of its axioms are universally quantified, and thus trivially satisfied if no set exists. The cardinality of the set of natural numbers, aleph null (), has many of the properties of a large cardinal. Thus the axiom of infinity is sometimes regarded as the first large cardinal axiom, and conversely large cardinal axioms are sometimes called stronger axioms of infinity. See also Peano axioms Finitism References Paul Halmos (1960) Naive Set Theory. Princeton, NJ: D. Van Nostrand Company. Reprinted 1974 by Springer-Verlag. . Thomas Jech (2003) Set Theory: The Third Millennium Edition, Revised and Expanded. Springer-Verlag. . Kenneth Kunen (1980) Set Theory: An Introduction to Independence Proofs. Elsevier. . Axioms of set theory Infinity