[FOM] links between nonstandard analysis and formal logic and set theory

[Alasdair Urquhart]

There are two recent books that provide useful discussions of nonstandard
analysis and set theory, and in particular, comparisons of the various
approaches.

The first is "Nonstandard Analysis, Axiomatically," by
Kanovei and Reeken.  It is mostly devoted to developing Hrbacek set
theory in detail, but also includes discussion of Nelson's internal
set theory, Kawai's nonstandard set theory, and a great deal more.

The second book is "Infinitesimal Analysis" by Gordon, Kusraev
and Kutateladze.  The first three chapters of this book are
a very readable historical survey of infinitesimals, a chapter
on naive foundations of infinitesimal analysis, and a chapter
on set-theoretical formalisms including Nelson's work and
a theory of their own called Nonstandard Class Theory.