AngularJS radio buttons on ngRepeat

Bar baz

HTML

<form name="myForm" ng-controller="MyCtrl">
    <p>Favorite Beatle</p>
    <ul>
        <li ng-repeat="person in people">
            <label>{{person.name}}
                <input type="radio" ng-model="$parent.name" name="name" value="{{person.name}}" required />
            </label>
        </li>
    </ul>
    <p><tt>myForm.$invalid: {{myForm.$invalid}}</tt></p>
    <button ng-disabled="myForm.$invalid">Submit</button>
</form>

JavaScript

function MyCtrl($scope) {
    $scope.people = [{
        name: "John"
    }, {
        name: "Paul"
    }, {
        name: "George"
    }, {
        name: "Ringo"
    }];
}