How far can we say that "All My Sons" is a tragedy?

I think Arthur Miller's play "All My Sons" perfectly fits with most of the definitions of tragedy. The first thing that makes this play a tragedy is the tragic event that has happened before the play stars - Larry's death. Joe has made a terrible mistake and he has to cope with the consequences. He is the tragic character as his family gets destroyed. "All My Sons" also fits a definition of tragedy because of the belief in stars and fate - Frank has made a horoscope and Kate wants to believe in it. Another fact that this is a tragedy is the time scale - all the events happen within 24 hours time. Even though Larry's character or ghost never appears, his presence can be felt all the time. Justification is another thing which makes "All My Sons" a tragedy. Joe knows he has done a terrible mistake, but he wants everyone to believe he has done it for the sake of his family. The play has a death theme in it - first, Larry kills himself, but at the end Joe takes his life away. The connection between the deaths is very strong, since Larry killed himself because he couldn't face his father anymore, but Joe commited a suicide after he got to know the reason of his son's death.