"The man has a big nose."

Translation: Ο άντρας έχει μία μεγάλη μύτη.

[PhilSimmonds]

why is one alternative without the indefinite article?

[troll1995]

The indefinite article is not required in greek when there could be more than one of the noun. The man could not have 2 noses, so no indefinite rticle is required (and using it with a certain tone results in emphasis). If you say έχω μεγάλη μύτη=i have a big nose (as a statement), έχει μια μεγάλη μύτη (with emphasis on μια)= he has a big nose (in a sense like "what a big nose he has!")

[PhilSimmonds]

very helpful- thanks