After chat this is the final answer.
$str = file_get_contents('put url here');
$json = json_decode($str, true);
$day = "";
if($json['mon'] == 1){$day = $day."MON,";}
if($json['tue'] == 1){$day = $day."tue,";}
if($json['wed'] == 1){$day = $day."wed,";}
if($json['thu'] == 1){$day = $day."thu,";}
if($json['fri'] == 1){$day = $day."fri,";}
if($json['sat'] == 1){$day = $day."sat,";}
if($json['sun'] == 1){$day = $day."sun";}
print_r($day) .'<br />';
EDIT 2 Using array
$str = file_get_contents('put url here');
$json = json_decode($str, true);
$day2=array();
if($json['mon'] == 1){array_push($day2 , "MON";}
if($json['tue'] == 1){array_push($day2 , "tue";}
if($json['wed'] == 1){array_push($day2 , "wed";}
if($json['thu'] == 1){array_push($day2 , "thu";}
if($json['fri'] == 1){array_push($day2 , "fri";}
if($json['sat'] == 1){array_push($day2 , "sat";}
if($json['sun'] == 1){array_push($day2 , "sun";}
print_r($day2);