I have no particular information about S.W.P.Steen. In his
book's preface, he wrote that drafts were read by Roger
Harrop, N.Routledge, G.T.Kneebone, T.J.Smiley and L.Drake;
from these colleagues, therefore, more information might be
had. From the time that the book had appeared, I remember an
English colleague to mention that Steen lived in Australia.
The book "Mathematical Logic, with special reference to the natural
numbers" appeared in 1972 and has ISBN 0 521 08053 3 . From
the start on, the author uses the technique of Lambda-terms,
and with it he proceeds first from propositional to
quantifier calculi and then discusses in detail (fragments
of) arithmetic, partly with omega rules, and their
incompleteness and unprovability results. Further topics
include degrees of unsolvability, the arithmetical
hierarchy, and non-standard models. The presentation is
technically elegant and quite detailed, but rather short on
motivations.
For a reader, having been brought up on the current fare of
books starting from a more model theoretical orientation
(Mendelsson 1964, Bell & Machover 1967), Steen's book may
appear as unusual and difficult. Indeed, it will hardly fit
as accompanying text for a current standard logic course.
The more so, it should challenge the inquiring mind who
will find rich rewards for his efforts.
WF