Extracting all cities from a state using PostGIS

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The reason that not all cities in Germany have an admin_level of 8 is that there are some "kreisfreie Städte" which use admin_level 6 (and, outside of Baden-Württemberg, even two "Stadtstaaten" which use admin_level 4).

Finding the cities that do not have an admin_level 8 tag but instead an admin_level 6 tag could be done like this:

SELECT a.*
FROM planet_osm_polygon a
LEFT OUTER JOIN planet_osm_polygon b
ON ST_COVERS(a.way,b.way) AND b.boundary='administrative' AND b.admin_level='8'
WHERE a.boundary='administrative' AND a.admin_level='6' AND b.osm_id IS NULL

The "left outer join" instructs PostgreSQL to find pairs of adminlevel 6/8 entities where the adminlevel 6 entity covers the adminlevel 8 entity, and to set the adminlevel 8 entity to NULL if none is found matching this criterion. Then, we only select those adminlevel 6 entities where the adminlevel 8 part is NULL, i.e. those that have no "children" on admin_level 8.