Building an SQL query string

How can I write this PHP code better? It puts together an SQL query string from user input. The task is to return search results based on one or more text fields. The user can determine if partial matches are allowed.

$compop = $allowpartial ? "LIKE" : "="; // use LIKE for wildcard matching
$any = $allowpartial ? "%" : ""; // SQL uses % instead of * as wildcard

$namecondstr    = ($name === "")    ? "TRUE" : ("Name    $compop '$any$name$any'");
$citycondstr    = ($city === "")    ? "TRUE" : ("City    $compop '$any$city$any'");
$itemnocondstr  = ($itemno === "")  ? "TRUE" : ("ItemNo  $compop '$any$itemno$any'");
$ordernocondstr = ($orderno === "") ? "TRUE" : ("OrderNo $compop '$any$orderno$any'");
$serialcondstr  = ($serial === "")  ? "TRUE" : ("Serial  $compop '$any$serial$any'");

$sortstr = ($name !== "") ? "Name" :
           (($city !== "") ? "City" :
           (($itemno !== "") ? "ItemNo" :
           (($orderno !== "") ? "OrderNo" :
                                    "Serial")));

$query = "SELECT * From Licenses
          LEFT JOIN Items
            ON Licenses.LicenseID = Items.LicenseID
          WHERE $namecondstr 
            AND $citycondstr 
            AND $itemnocondstr 
            AND $ordernocondstr
            AND $serialcondstr
          ORDER BY $sortstr, Licenses.LicenseID";

Use Prepared Statements

Your code is vulnerable to SQL injection attacks. Use PDO or mysqli prepared statements to avoid this. See this answer for how to use PDO for this. If you are using mysql_* you should know that it is already in the deprecation process.
Miscellaneous

• Consider using empty to check for empty strings (see comment from Corbin below).

• Personally I would use an if else rather than have two identical ternary conditions.

StackExchange Code Review Q#19128, answer score: 6