success: function(response) {
  if(response.success == 1) {
    alert('success');
    if(typeof $row == 'undefined' ) {
      alert('undefined!'); // this alert does not come up
    } else {
      alert('the $row var is defined'); // this alert DOES come up
      $row.html('hahaha'); // this works, the contents of the row are replaced
      $row.remove(); // this doesn't work. The row is still there, with 'hahaha'
    }
  } else {
    alert('failed');
  }
}

$(document).on("click",".allowed_val_delete",function() { // 20150328
    var $this_row = $(this).closest('tr');
    var allowed_val_id = $this_row.attr("id").split('_')[1];
    var data = new Object();
    //alert('Delete allowed value with id "' + allowed_val_id + '"');
    data.action = 'DELETE';
    data.id = parseInt(allowed_val_id,10);
    $this_row.hide(); // hide row immediately. Show it again if ajax fails.

    $.ajax({
        data: data,
        //type: "POST",
        type: "POST", // 20150502 experimenting with other HTTP methods. (method is alias for type but requies jquery 1.9+)
        url: "controllers/core_fields/ajax/allowed_values.php",
        dataType: "json",
        success: function(response) {
            if(response.success == 1) {
                //alert('Removing row');
                if(typeof $this_row == 'undefined') {
                    alert('$this_row with val_id = ' + allowed_val_id + ' is undefined');
                } else {
                    //alert('$this_row with val_id = ' + allowed_val_id + ' is defined');
                    $this_row.remove(); // doesn't work
                }
                /*var index = allowed_value_ids.indexOf(allowed_val_id);
                allowed_value_ids.splice(index,1); // remove from the list of ids*/
                $("#maintable").tablesorter().trigger("update"); // updates sorting
                $("#maintable").tablesorter().trigger("appendCache"); // updates sorting
            } else {
                alert('Failed to remove');
                $this_row.show();
            }
            //alert('action: ' + response.action + '; id: ' + response.id);
            //alert(response);
        }
    });

});