In ruby I would use something like
"PostgreSQL".downcase.start_with?("p")
=> true
and the equivalent in a query would be:
select lower(left('PostgreSQL', 1)) = 'p';
?column?
----------
t
(1 row)
and if you have the citext extension enabled you could do:
select left('PostgreSQL', 1)::citext = 'p';
?column?
----------
t
(1 row)
Other things:
select *
from users
where left(display_name, 1)::citext = 'a'
;