How to alias a field or column in MySQL?

Consider using a subquery, like:

SELECT col1
,      col1 + field3 AS col3 
FROM   (
       SELECT  field1 + field2 as col1
       ,       field3
       from    core
       ) as SubQueryAlias

You can select the alias:

SELECT SUM(field1 + field2) AS col1, (select col1) + field3 AS col3 from core

This works.

select @code:= SUM(field1 + field2), @code+1 from abc;

But, please be aware of the following (from the MySQL 5.6 docs):

As a general rule, other than in SET statements, you should never assign a value to a user variable and read the value within the same statement. For example, to increment a variable, this is okay:

SET @a = @a + 1;

For other statements, such as SELECT, you might get the results you expect, but this is not guaranteed. In the following statement, you might think that MySQL will evaluate @a first and then do an assignment second:

SELECT @a, @a:=@a+1, ...;

However, the order of evaluation for expressions involving user variables is undefined.

So, use at your own risk.