[FOM] Real Numbers

Victor Makarov viktormakarov at hotmail.com
Sun May 4 18:59:47 EDT 2003

>Debates over Benacerraf's problem always seem to lead to someone's 
>something like the following, which Wiman says here:
>>The real numbers are not equivalence classes of Cauchy sequences.  They 
>>can be, but they can also be Dedekind cuts, binary numbers, real closed 
>>fields, one dimensional continua, or a number of other things.
>I always feel puzzled when I get to that point, however. ...
>Richard Heck

It seems that some authors have mixed together entirely different concepts:

1) the concept of "abstract reals" that can be represented by the theory TR 
of the field R of real numbers;

2) the concept of a model of the theory TR;
(each model of TR introduces "concrete reals");

Some well-known (different) models of the theory TR are "Dedekind cuts" and 
"Cauchy sequences".

Victor Makarov

The new MSN 8: smart spam protection and 2 months FREE*  

More information about the FOM mailing list