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sql - Is it possible to perform a bitwise group function?

I have a field in a table which contains bitwise flags. Let's say for the sake of example there are three flags: 4 => read, 2 => write, 1 => execute and the table looks like this*:

  user_id  |  file  |  permissions
-----------+--------+---------------
        1  |  a.txt |  6    ( <-- 6 = 4 + 2 = read + write)
        1  |  b.txt |  4    ( <-- 4 = 4 = read)
        2  |  a.txt |  4
        2  |  c.exe |  1    ( <-- 1 = execute)

I'm interested to find all users who have a particular flag set (eg: write) on ANY record. To do this in one query, I figured that if you OR'd all the user's permissions together you'd get a single value which is the "sum total" of their permissions:

  user_id  |  all_perms
-----------+-------------
        1  |  6        (<-- 6 | 4 = 6)
        2  |  5        (<-- 4 | 1 = 5)

*My actual table isn't to do with files or file permissions, 'tis but an example

Is there a way I could perform this in one statement? The way I see it, it's very similar to a normal aggregate function with GROUP BY:

SELECT user_id, SUM(permissions) as all_perms
FROM permissions
GROUP BY user_id

...but obviously, some magical "bitwise-or" function instead of SUM. Anyone know of anything like that?

(And for bonus points, does it work in oracle?)

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MySQL:

SELECT user_id, BIT_OR(permissions) as all_perms
FROM permissions
GROUP BY user_id

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