Of course the values you assign don’t have to be a boolean like the example, it could be anything, like 'yes' and 'no' or whatever you want the result to be. Or perform some action/function depending on it being set.
If there is a whole load of checkboxes, you may automate it with an array of the input names:-
$checkboxes = array('firstbox', 'secondbox', 'anotherbox', 'onemorebox'); // Names of inputs
foreach($checkboxes as $checkbox){ // Check them all
if(isset($_POST[$checkbox])){ $boxresults[$checkbox] = true ;}
else{ $boxresults[$checkbox] = false ;}
}