A Zoozone 1 or similar sized tank type cage such as katiepillow already suggested are good minimums for syrians.
The only acceptable barred cage that won't take up huge amounts of room are the savic cambridge, cant remember the dimensions of it. Though it is a highly debated topic, some say its ok, some say it is too small. Having seen one I would say it was too small, but I know other people get on OK with it.
Then slightly more space (80cmx40cm) are cages like the ferplast mary, the savic ruffy, the hamster heaven. all approx the same thing. The bigger barred cages are the only ones I have listed that could be stacked and save space potentially, unfortunately the cambridge has a curved roof.