Rulers of the emirate used the title "emir" or "sultan" until the 10th century, when Abd al-Rahman III was faced with the threat of invasion by the Fatimid Caliphate. To aid his fight against the invading Fatimids, who claimed the caliphate in opposition to the generally recognised Abbasid Caliph of Baghdad, Al-Mu'tadid, Abd al-Rahman III claimed the title of caliph himself. This helped Abd al-Rahman III gain prestige with his subjects, and the title was retained after the Fatimids were repulsed. The rule of the Caliphate is considered as the heyday of Muslim presence in the Iberian peninsula, before it fragmented into various taifas in the 11th century. This period was characterised by a flourishing in technology, trade and culture; many of the buildings of al-Andalus were constructed in this period.