Description: The equivalence of two versions of the Generalized Continuum Hypothesis.
The right-hand side is the standard version in the literature. The
left-hand side is a version devised by Kannan Nambiar, which he calls
the Axiom of Combinatorial Sets. For the notation and motivation behind
this axiom, see his paper, "Derivation of Continuum Hypothesis from
Axiom of Combinatorial Sets", available at
http://www.e-atheneum.net/science/derivation_ch.pdf . The
equivalence of the two sides provides a negative answer to Open Problem
2 in
http://www.e-atheneum.net/science/open_problem_print.pdf .
The key idea in the proof below is to equate both sides of alephexp2 to the successor aleph using enen2 . (Contributed by NM, 1-Oct-2004)