Register with PDO

<?php
  session_start();
  $pdo = new PDO('mysql:host=localhost;dbname=test', '', '$') //last two are removed for safety reasons
?>
<html>
 <head>
        <meta name='viewport' content='width=device-width, initial-scale=1'>
        <meta charset="utf-8">
        <title>Regsiter</title>
 </head>
 <body>

        <h3>Register</h3>

        <?php
        $showFormular = true;

        if(isset($_GET['register']))   {
         $error = false;
         $user = $_POST['user'];
         $password = $_POST['password'];
         $password2 = $_POST ['password2'];

         if(strlen($password) === 0) {
             echo 'Please enter a password!';
             $error = true;
         }
         if($password != $password2) {
             echo 'The passwords do not match, please try again!';
             $error = true;
         }
         if(!$error) {
             $statement = $pdo->prepare("SELECT * FROM userdaten WHERE user = '".$user."' ");
              $result = $statement->execute(array('user' => $user));
              $user = $statement->fetch();

              if($user !== false) {
                  echo 'Username is already taken<br>';
                  $error = true;
              }
            }
            if(!$error) {
                $password_hash = password_hash($password, PASSWORD_DEFAULT);

                $statement = $pdo->prepare("INSERT INTO userdaten (user, password) VALUES ('".$user."','".$password."')");
                $result = $statement->execute(array('user' => $user, 'password' => $password_hash));

                if($result) {
                    echo 'You are succesfully registered, you can <br> <a href="login.php">login</a> now!';
                }
            }
        }
        if($showFormular) {
        ?>
         <form action="?register=1" method="post">
         Username: <br />
         <input type="text" size="40" maxlength="25" name="user" />
         <br />
         Password: <br />
         <input type="password" size="40" maxlength="255" name="password" />
         <br />
         Repeat your password: <br />
         <input type="password" size="40" maxlength="255" name="password2">
         <br />
         <input type="submit" value="Register">
         </form>
         <?php
         }
          ?>

 </body>
</html>