[FOM] H.N. from "Mathematical Cranks"

[A. Mani]

On Sun, May 6, 2018 at 1:26 AM, tchow <tchow at alum.mit.edu> wrote:
> In Underwood Dudley's book "Mathematical Cranks," he devotes a short chapter
> to someone that he identifies only as "H.N."  Evidently, H.N. was a full
> professor of mathematics when, in 1970, he wrote:
>
> "Recently I have discovered a surprising fact.  Logicians' axiomatic set
> theory is meaningless in mathematics.  They have been working in wrong
> mathematics and exerting their efforts in vain over the past sixty years.
> They are still making the same mistake.  So I dare say that all the books
> related to axiomatic set theory must be removed immediately.  Only my book
> describes correct set theory."
>

I found exactly one book on 'set theory' written by an author with
initials 'H.N.' before 1970:

Norman Hamilton and Joeseph Landin (Univ of Illnois):
Set Theory and the Structure of Arithmetic, Allyn and Bacon, 1964, 292pp

The book in question is meant for high school teachers and is written
in fairly simple terms.
The natural numbers are defined using sets and the finite induction principle.
Concept of hereditary sets, final elements in a set, etc are introduced.
Authors use transfinite induction in the book, but claim to avoid it
in the earlier part.
Cantor sequences are used to define the reals instead of Dedekind cuts.
There are few bad typos in the book E.g p 117

Some results do not require transfinite induction, but they do use it
in proving them.

Overall a simple, readable, standard text.


Best

A Mani

Prof(Miss) A Mani
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