SQL statement to generate a column whose value is the record index

I have some SQL table, say with a single column c1:

Now, I'd like to issue an SQL command (not some operation of my DBMS, which I have intentionally not mentioned) which causes my table to be:

Very simple... can this be done? Obviously, you don't know in advance the length of the table, so no SQL insertion or similar tricks.

Note: I'd like a general answer, but to be specific - I'm working with MonetDB.

Inspired by @a_horse_with_no_name 's answer...:

SELECT 
  c1, 
  row_number() OVER (ORDER BY dummy)-1 AS record_index
FROM 
  (SELECT 
    c1,
    42 AS dummy 
  FROM t1
) AS t1_augmented;

_{(Noting of course that row_number()'s result is 1-based.)}