Arnold Arons let me down by not discussing inertial
frames in his fine book.
Depends upon which fine book you mean. There are *four*
separate citations in his index for "inertial frame" in
his 1965 textbook "Development of Concepts of Physics".
It is curious that the first citation (p. 124) is at
the correct place to define the inertial frame, but the
words "inertial frame" do not appear on that page. They
are used in the subsequent citations, however. Arons
may have been torn on this issue as well. It is clear
that he needed the concept to develop later material.
This book is one of my treasures. It is too good for
ordinary students (and uses language appropriate to a
university level), but it is nice to have on the shelf
for browsing when one is looking for a lecture
inspiration.