Learn Danish: Mange bygninger i byen er faldefærdige nu. - Many buildings in the city are dilapidated now.

You would insert the infinitive verb blive (to become) into the construction: Mange bygninger i byen er ved at blive faldefærdige nu. This translates to 'Many buildings in the city are in the process of becoming dilapidated now,' perfectly capturing the ongoing transition taught in this lesson.

The word faldefærdige is quite long. What are its root parts?

It is a compound of the verb falde (to fall) and the adjective færdig (ready or finished). Literally, a building that is faldefærdig is 'ready to fall.' It is a very descriptive and common way to say dilapidated or ramshackle in Danish!

Just as a quick refresher, why does faldefærdige end in -e here?

Danish adjectives must agree in number with the noun they describe. Because the subject of the sentence is plural (Mange bygninger), the adjective takes the plural -e ending. If we were talking about a single building, it would simply be faldefærdig.

Could I just say i by instead of the definite i byen here?

No. While Danish drops the definite article for some institutional locations (like i skole for 'in school' or i kirke for 'in church'), referring to the physical infrastructure of a specific town or city requires the definite form byen. Note that i byen is also used as an idiom for 'out on the town' (clubbing/drinking), but the context of buildings makes the literal meaning obvious here.