Combining values in a column

I have a query which returns a single column of integers which I want
to combine together with &, "bitwise AND". Basically it's a simple
list of access levels that a user might have and I want to merge the
list into one value. There can be zero, one or more values in the list
so I have to be able to cope with the no-results .

For example

access
--------
31
511

Would lead to 31 & 511 which gives 31.

I guess really this can lead to the more generic question. How do I
apply a general function to combine the values, if I, for example,
wanted to write my own aggregate function like sum?

Thanks in advance,

Stephen Quinney