Я не знаю, что в PHP, но это работает:
> db.items.find({})
{ "_id" : ObjectId("4ea98d0fa287fedc0281feee"), "name" : "first", "keywords" : [ "one", "two", "three", "four" ] }
{ "_id" : ObjectId("4ea98d1aa287fedc0281feef"), "name" : "first", "keywords" : [ "two", "three", "four", "five" ] }
{ "_id" : ObjectId("4ea98d23a287fedc0281fef0"), "name" : "first", "keywords" : [ "four", "five", "six" ] }
{ "_id" : ObjectId("4ea99243a287fedc0281fef1"), "name" : "first", "keywords" : [ "five", "six" ] }
{ "_id" : ObjectId("4ea99247a287fedc0281fef2"), "name" : "first", "keywords" : [ "five", "six", "seven" ] }
{ "_id" : ObjectId("4ea99273a287fedc0281fef3"), "name" : "first", "keywords" : [ "one", "two", "seven" ] }
{ "_id" : ObjectId("4ea9927aa287fedc0281fef4"), "name" : "first", "keywords" : [ "one", "two", "seven" ] }
> db.items.find({$or:[{keywords:"four"},{keywords:"five"}]})
{ "_id" : ObjectId("4ea98d0fa287fedc0281feee"), "name" : "first", "keywords" : [ "one", "two", "three", "four" ] }
{ "_id" : ObjectId("4ea98d1aa287fedc0281feef"), "name" : "first", "keywords" : [ "two", "three", "four", "five" ] }
{ "_id" : ObjectId("4ea98d23a287fedc0281fef0"), "name" : "first", "keywords" : [ "four", "five", "six" ] }
{ "_id" : ObjectId("4ea99243a287fedc0281fef1"), "name" : "first", "keywords" : [ "five", "six" ] }
{ "_id" : ObjectId("4ea99247a287fedc0281fef2"), "name" : "first", "keywords" : [ "five", "six", "seven" ] }
> db.items.find({keywords:{$in:["four","five"]}})
{ "_id" : ObjectId("4ea98d0fa287fedc0281feee"), "name" : "first", "keywords" : [ "one", "two", "three", "four" ] }
{ "_id" : ObjectId("4ea98d1aa287fedc0281feef"), "name" : "first", "keywords" : [ "two", "three", "four", "five" ] }
{ "_id" : ObjectId("4ea98d23a287fedc0281fef0"), "name" : "first", "keywords" : [ "four", "five", "six" ] }
{ "_id" : ObjectId("4ea99243a287fedc0281fef1"), "name" : "first", "keywords" : [ "five", "six" ] }
{ "_id" : ObjectId("4ea99247a287fedc0281fef2"), "name" : "first", "keywords" : [ "five", "six", "seven" ] }