Edit
All-in-one version
<?php
if(isset($_POST['address_building_number']) || !empty($_POST['address_building_number'])){
$address_building_number = $_POST['address_building_number'];
echo 'Greetings';
$farewell = 'Farewell';
}
echo $address_building_number;
echo $farewell;
// comment out exit; if you want the form to NOT appear after submit
// exit;
?>
<form action="" method="post">
Name: <input type="text" name="address_building_number"><br>
<input type="submit" value="Submit">
</form>
Original answer
Your conditionals appear to contradict each other.
Observe the if(isset and if(!isset for the
$_POST['address_building_number']
The issue here is, "if it IS set and if it is NOT set"; creating a conflicting statement.
You likely intended to use:
if(isset($_POST['address_building_number']) OR !empty($_POST['address_building_number']))
(Just an FYI) If that's correct, || takes precedence over OR, so use:
if(isset($_POST['address_building_number']) || !empty($_POST['address_building_number']))
...which checks if it is set or not empty.
The following has been tested successfully and everything echoed without errors:
HTML
<form action="action.php" method="post">
Name: <input type="text" name="address_building_number"><br>
<input type="submit" value="Submit">
</form>
PHP (action.php) as an example
<?php
if(isset($_POST['address_building_number']) || !empty($_POST['address_building_number'])){
$address_building_number = $_POST['address_building_number'];
echo 'Greetings';
$farewell = 'Farewell';
}
echo $address_building_number;
echo $farewell;
?>
Regarding the request to "define the index while still being able to echo Greetings and Farewell" - The intent behind this is unclear.
If by that you mean, "if you can still echo "Greetings and Farewell" outside of that conditional statement", then the response is affirmative; aligning with what my answer accomplishes, using the OR (||) operator. Had it been the AND (&&) operator, this wouldn't be feasible.