PHP Cannot use a scalar value as an array - Incrementing a session - php

Question

I am writing a script to place an order which will be added to a cart, I am storing the selected values for the cart as a session. Each new selection (addition to the cart) is added to a new session which is incremented by one each time.
ie.
$_SESSION['cart'][1]
$_SESSION['cart'][2]
$_SESSION['cart'][3]
I am receiving the below error and am stumped.
Warning: Cannot use a scalar value as an array in C:\wamp\www\php\cart\carting\order.php on line 37 -(This is the line $_SESSION['cart'][$p] = $cartstring;)
<?PHP
session_start();
$productlist = $_POST['products']; //Form post
if (isset($productlist)) {
if (!isset($_SESSION['cart'])) {
$p = 0;
$_SESSION['cart'][$p];
print $_SESSION['cart'][$p];
}
elseif (isset($_SESSION['cart'])) {
$p = count($_SESSION['cart']);
$p++;
$product = explode('-', $productlist[1][0]);
$productname = $product[0];
$productprice = $product[1];
$productqty = $productlist[1][1];
$itemsubtotal = ($productprice * $productqty);
$cartstring = "productid-$productname-$productprice-$productqty-$itemsubtotal";
$_SESSION['cart'][$p] = $cartstring; //THIS IS LINE 37
}
}
$product1 = "Bread";
$price1 = 12;
$product2 = "Butter";
$price2 = 2;
print '<form action="order.php" method="post">';
print '<input type="checkbox" name="products[1][]" value="'.$product1." "."-"." ".$price1.'" />';echo $product1;
print '<input type="text" name="products[1][]" value="" />QTY';print '<br>';
print '<br>';print '<br>';
print '
<input type="submit" name="formSubmit" value="Submit" />
</form>';
?>