1. The Denumerable Axiom of Choice has also been called the Countable Axiom of Choice (see Jech 1973, 20). However, we distinguish sharply between a denumerable set and one that is countable, i.e., finite or denumerable.
2. Jensen 1966, 294.
3. Bernays 1942, 86. The name of this principle is due to Tarski [1948, 96]. Azriel Levy [1964, 136] generalized it from sequences of type ω to sequences of type α for any infinite ordinal α.
4. See for example Kleene and Vesley 1965, Heyting 1966, Bishop 1967, and Gauthier 1977.
5. In the mathematical literature the term point-set topology is ambiguous. Within this book it refers to the theory, sometimes called Mannigfaltigkeitslehre or the theory of point-sets, that Cantor originated and that utilized such notions as limit point, closed set, and derived set in ℝ n . Largely through the work of Hausdorff, this theory later grew into general topology, which considered more general spaces.