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Well, yes and no.
As in many European languages, the word for "one" (ένας/μία (μια)/ένα) doubles as the indefinite article: ο σκύλος: "the dog", ένας σκύλος: "one dog" or "a dog" depending on context (as in English, and unlike for instance French, there's no plural equivalent: οι σκύλοι: "the dogs", σκύλοι: "dogs").
That said, there are also plenty of cases where English will use the indefinite article while the equivalent Greek won't. For instance, in English you say "I am a doctor", while in Greek you'll simply say είμαι γιατρός. Saying είμαι ένας γιατρός sounds to me like "I'm just *one* doctor", i.e. I can't do this alone. It emphasises that the doctor is just one person. In any case, it would be incorrect if you just wanted to say "I am a doctor".
Another example is a construction like "once a day". In Greek, you'll use the definite article here (and the accusative case to boot!): μία φορά τη μέρα.
To sum it up: Modern Greek has an indefinite article, which just happens to be the word for "one", just as in many other European languages. However, it's not used in all cases where the indefinite article is used in English. When is it used and when not? Here's a small rule of thumb: if in the English sentence you can replace "a" by "one" and it doesn't change the overall meaning of the sentence, you can use ένας in Greek. If you replace "a" by "one" and it completely changes the meaning (just like "I am one doctor" is quite a different thing from "I am a doctor", and "once one day" is completely different from "once a day"), you cannot use ένας. Like all rules of thumb it's a bit rough around the edges, and may have exceptions, but it should work in most cases.
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