これはうまくいくはずです
db.test.find({$or:[{a:{$size:0}},{"a.0":{$exists:true}}]})
a
フィールドに0
キーを含むオブジェクトが含まれていないことを確認してください。
例えば
> db.test.find()
{ "_id": ObjectId("5059ac3ab1cee080a7168fff"), "bar": [ "baz", "", "qux" ] }
{ "_id": ObjectId("5059ac48b1cee080a7169000"), "hello": 1, "bar": false, "world": 34 }
{ "_id": ObjectId("5059ac53b1cee080a7169001"), "hello": 1, "world": 42 }
{ "_id": ObjectId("5059ac60b1cee080a7169002"), "hello": 13, "bar": null, "world": 34 }
{ "_id": ObjectId("5059ac6bb1cee080a7169003"), "hello": 133, "bar": [ ], "world": 334 }
{ "_id": ObjectId("5059b36cb1cee080a7169004"), "hello": 133, "bar": [ "" ], "world": 334 }
{ "_id": ObjectId("5059b3e3b1cee080a7169005"), "hello": 133, "bar": "foo", "world": 334 }
{ "_id": ObjectId("5059b3f8b1cee080a7169006"), "hello": 1333, "bar": "", "world": 334 }
{ "_id": ObjectId("5059b424b1cee080a7169007"), "hello": 1333, "bar": { "0": "foo" }, "world": 334 }
> db.test.find({$or: [{bar: {$size: 0}}, {"bar.0": {$exists: true}}]})
{ "_id": ObjectId("5059ac3ab1cee080a7168fff"), "bar": [ "baz", "", "qux" ] }
{ "_id": ObjectId("5059ac6bb1cee080a7169003"), "hello": 133, "bar": [ ], "world": 334 }
{ "_id": ObjectId("5059b36cb1cee080a7169004"), "hello": 133, "bar": [ "" ], "world": 334 }
{ "_id": ObjectId("5059b424b1cee080a7169007"), "hello": 1333, "bar": { "0": "foo" }, "world": 334 }