What is the PHP equivalent of Javascript's undefined?

Not really, undefined has no counterpart in PHP. Comparing JS's undefined to PHP s null doesn't really stack up, but it's as close as you're going to get. In both languages you can assign these values/non-values:

var nothingness = undefined;
$nothing = null;

and, if you declare a variable, but don't assign it anything, it would appear that JS resolves the var to undefined, and PHP resolves (or assigns) that variable null:

var nothingness;
console.log(nothingness === undefined);//true

$foo;
echo is_null($foo) ? 'is null' : '?';//is null

Be careful with isset, though:

$foo = null;
//clearly, foo is set:
if (isset($foo))
{//will never echo
    echo 'foo is set';
}

The only real way to know if the variable exists, AFAIK, is by using get_defined_vars:

$foo;
$bar = null;
$defined = get_defined_vars();
if (array_key_exists($defined, 'foo'))
{
    echo '$foo was defined, and assigned: '.$foo;
}

I don't think there is undefined. Rather than checking if something is undefined as you would in JavaScript:

if(object.property === undefined) // Doesn't exist.

You just use isset():

if(!isset($something)) // Doesn't exist.

Also, I think your understanding of undefined is a little odd. You shouldn't be setting properties to undefined, that's illogical. You just want to check if something is undefined, which means you haven't defined it anywhere within scope. isset() follows this concept.

That said, you can use unset() which I guess would be considered the same as setting something to undefined.