I save a string set in the shared preferences, if I read it out it\'s ok. I start other activities, go back and read it again, it\'s ok. If I close the application, and start it
Based on your question, you should call commit only after 4 items have been added to the set. In your code, you are calling commit for each feedback which will overwrite the previous feedback.
Update: http://developer.android.com/reference/android/content/SharedPreferences.html#getStringSet(java.lang.String, java.util.Set)
Note that you must not modify the set instance returned by this call. The consistency of the stored data is not guaranteed if you do, nor is your ability to modify the instance at all.
This is exactly what you are doing