[FOM] Wildberger on Foundations

Arnon Avron aa at tau.ac.il
Tue Jul 17 07:05:39 EDT 2012

On Wed, Jul 11, 2012 at 12:51:02PM -0400, joeshipman at aol.com wrote:
> In his discussion with me, he asks for examples of texts where the
> modern framework of Analysis is developed completely rigorously from
> first principles. 
> Can anyone suggest some source books that might satisfy his request?

Here are two books which were used as the main textbooks in undergrduate 
courses I took about 40 years ago in Tel-Aviv university, and come
close to this ideal:

G. M. Fikhtengol'ts: The fundamentals of Mathematical Analysis 

  This is the book from which I have learned Analysis. It
  starts with a rigorous  introduction of the real numbers as 
  Dedekind cuts, and continue to provide rigorous definitions and proofs 
  in both of its two comprehensive volumes. It does not provide a list of 
  "basic principles", though.

J. Dugundji: Topology   

   This book is not a book in analysis. However, it is relevant here
  because it is almost fully self-contained. It starts from elementary 
  set theorys, and it  even provides a full list of axioms (GB in an 
  informal form).

And I should mention of course also Feferman's classic book on the
number systems.

Arnon Avron

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