PostgreSQL - repeating rows from LIMIT OFFSET

For more details from PostgreSQL documentation (http://www.postgresql.org/docs/8.3/static/queries-limit.html) :

When using LIMIT, it is important to use an ORDER BY clause that constrains the result rows into a unique order. Otherwise you will get an unpredictable subset of the query's rows. You might be asking for the tenth through twentieth rows, but tenth through twentieth in what ordering? The ordering is unknown, unless you specified ORDER BY.

The query optimizer takes LIMIT into account when generating a query plan, so you are very likely to get different plans (yielding different row orders) depending on what you give for LIMIT and OFFSET. Thus, using different LIMIT/OFFSET values to select different subsets of a query result will give inconsistent results unless you enforce a predictable result ordering with ORDER BY. This is not a bug; it is an inherent consequence of the fact that SQL does not promise to deliver the results of a query in any particular order unless ORDER BY is used to constrain the order.

Why does "foo" appear in both queries?

Because all rows that are returned have the same value for the status column. In that case the database is free to return the rows in any order it wants.

If you want a reproducable ordering you need to add a second column to your order by statement to make it consistent. E.g. the ID column:

SELECT students.* 
FROM students 
ORDER BY students.status asc, 
         students.id asc

If two rows have the same value for the status column, they will be sorted by the id.