Re: Implementable Set Theory and Consistency of ZFC

Marshall wrote:

On Oct 24, 3:57 am, "Jesse F. Hughes" <je...@xxxxxxxxxxxxx> wrote:

Han de Bruijn <Han.deBru...@xxxxxxxxxxxxxx> writes:

My "toy set theory" includes all set theory that is needed to build any
database applications. But it's nothing new in that respect.

In what sense can someone use set theory to build a database
application?

Set theory is the basis for SQL, which is the overwhelmingly
dominant query language for database systems. (Strictly
speaking, SQL tables are multisets but standard practice
is to use them as sets--always declaring uniqueness.)

Adding a primary key makes those multisets "almost" a single set.
As an example in my article, with the axiom of Specification.
Suppose we have the following table, called A :

key | color
-----------
1 | blue
2 | red
5 | red
7 | blue

Then we can create a subset B = {2,5}, with an SQL database query:
create table B as (select key from A where color = 'red');
This is the same as B = { x e A : C(x) } where C(x) = (color = 'red').

My interest in set theory is driven by my interest in data
management. (Well, it's pretty cool in its own right as well.)

Affirmative!

I am expressing no opinion on HdB's axioms or other arguments.
But on the question of whether there is a link between set
theory and database application, then: yeah, totally.

Observe for example:

http://en.wikipedia.org/wiki/Union_%28SQL%29

Thank you very much for jumping in.

Han de Bruijn

.

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