ch manuscript

[martdowd at aol.com]

FOM:
I have added the following to the end of the introduction to Some Arguments in Favor of the Continuum Hypothesis
 https://www.researchgate.net/publication/363885503
----------
Recently there has been considerable argument that certain axioms for
set theory, which imply $\fc=\aleph_2$, should be considered.
For example, the following statement is made in \cite{AspSch}.

\begin{quote}
As we shall now try to explain, in the light of our unifying result, Theorem
1.2, one could make the case that with the two axioms MM++ and $(*)$,
natural and strong such axioms have already been found.
\end{quote}

\cite{AspSch} goes on to say

\begin{quote}
One axiom that does settle the Continuum Problem is CH itself; after all, CH
looks natural in that it gives the least possible value to $2^{\aleph_0}$
\end{quote}

and then to state that ``CH is often regarded as
a minimalistic assumption'' which precludes ``maximality principles''
such as forcing axioms.

In this note it is argued that,
although ZFC places no bound on the cardinality of a well-order of the reals,
in fact the value is $\aleph_1$.
The arguments are simple and require only basic set theory
and some basic forcing theory.
----------

Mathematics Magazine rejected the manuscript as having too ,much mathematics; I'm submitting iy elsewhere.  Thanks to Tim Chow for his comments on the manuscripy.
Martin Dowd
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