Preferences.putStringSet() does not exist in Gingerbread so you can use this class below as a substitute if you need to target below Android v3.0 (Honeycomb)

JSONSharedPreferences

import org.json.JSONArray;
import org.json.JSONException;
import org.json.JSONObject;
import android.content.SharedPreferences;

public class JSONSharedPreferences {
  private static final String PREFIX = "json";

    public static void saveJSONObject(SharedPreferences prefs, String key, JSONObject object) {
        SharedPreferences.Editor editor = prefs.edit();
        editor.putString(JSONSharedPreferences.PREFIX+key, object.toString());
        editor.commit();
    }

    public static void saveJSONArray(SharedPreferences prefs, String key, JSONArray array) {
        SharedPreferences.Editor editor = prefs.edit();
        editor.putString(JSONSharedPreferences.PREFIX+key, array.toString());
        editor.commit();
    }

    public static JSONObject loadJSONObject(SharedPreferences prefs, String key) throws JSONException {
        return new JSONObject(prefs.getString(JSONSharedPreferences.PREFIX+key, "{}"));
    }

    public static JSONArray loadJSONArray(SharedPreferences prefs, String key) throws JSONException {
        return new JSONArray(prefs.getString(JSONSharedPreferences.PREFIX+key, "[]"));
    }

    public static void remove(SharedPreferences prefs, String key) {
        if (prefs.contains(JSONSharedPreferences.PREFIX+key)) {
            SharedPreferences.Editor editor = prefs.edit();
            editor.remove(JSONSharedPreferences.PREFIX+key);
            editor.commit();
        }
    }
}

Usage example

//Below, the code to use putStringSet is commented out. Alternative JSONSharedPreferences is used instead 

//Set<String> trainers = new TreeSet<String>();		
JSONArray jTrainers = new JSONArray();
List<FilteredWorkoutVideo> videos = getAllFilteredVideos(prefs);
for (FilteredWorkoutVideo video : videos) {
	//trainers.add(video.getTrainerName());	
  jTrainers.put(video.getTrainerName());
}

//e = prefs.edit();
//e.putStringSet(Constants.KEY_ALL_TRAINERS, trainers);
//e.apply();
JSONSharedPreferences.saveJSONArray(prefs, Constants.KEY_ALL_TRAINERS, jTrainers);