Axiomatic derivation of the continuum hypothesis (Q1963096)

The author provides a flawed definition of an operation \(m\otimes^k n\) for cardinal numbers \(m,n,k\) with \(k\leq\aleph_0\), on the basis of which he makes the unjustified claim that \(\aleph_1=\aleph_0\otimes^{\aleph_0}\aleph_0\). He uses this claim to derive the continuum hypothesis from his Axiom of Monotonicity.