FOM: ordered pair: Bourbaki

[Vedasystem@aol.com]

In a message dated 5/3/99 3:15:16 PM Eastern Daylight Time, Martin Davis 
writes:

> 
>  Abstract data types are fine so long as concrete implementations are
>  possible. And once you choose a particular implementation, extraneous
>  irrelevant facts will appear.
>  

Defining an abstract data type, one can (and usually does) hide its concrete 
implementation, so extraneous irrelevant facts cannot appear. One can also
define a pure abstract data type, without a concrete implementation. 
It is convenient because a pure abstract data type can have many 
different concrete implementations (as well as a theory can have many 
interpretations) -- a pure abstract data type is actually an axiomatic 
theory. 

Victor Makarov,  Brooklyn