Using ISSET with checkboxes

I am working on a wordpress search form to refine the current search and what Im trying to do is have the search results page with the search from and it's values set based on the query.

So far I've been successful in doing so with single select drop downs and single checkboxes like so --

<!-- SINGLE SELECT -->
    <select name="baths" class="form-control">
    <?php if (isset($_GET['baths'])) {
        $bths = $_GET['baths']; ?>
    <option value="<?php echo $bths; ?>"><?php echo $bths; ?></option>  
    <?php } else { ?>
    <option value="Any">Any</option>
    <?php } ?>
    <option value="Any">Any</option>
    <option value="1">1+</option>
    <option value="2">2+</option>
    <option value="3">3+</option>
    <option value="4">4+</option>
    <option value="5">5+</option>
    <option value="6">6+</option>
    <option value="7">7+</option>
    <option value="8">8+</option>
    <option value="9">9+</option>
    <option value="10">10+</option>
    </select>

<!-- SINGLE CHECKBOX -->
<input type="checkbox" name="dogs" class="styled" value ="yes" <?php if (isset($_GET['dogs'])) { ?>checked<?php } ?>>

That works, but for the multiple values it doesn't. This is my function to generate a set of checkboxes to select amenities -

<?php
$amenity_array = array();
$id            = get_query_var('site');
if (!empty($id)) {
  $property_amenities = get_post_meta($id, 'imic_property_amenities', true);
  global $imic_options;
  foreach ($property_amenities as $properties_amenities_temp) {
    if ($properties_amenities_temp != 'Not Selected') {
      array_push($amenity_array, $properties_amenities_temp);
    }
  }
}
global $imic_options;
if (isset($imic_options['properties_amenities']) && count($imic_options['properties_amenities']) > 1) {
  foreach ($imic_options['properties_amenities'] as $properties_amenities) {
    $am_name = strtolower(str_replace(' ', '', $properties_amenities));
    $check   = '';
    if (in_array($properties_amenities, $amenity_array)) {
      $check = 'checked="checked"';
    }

<!-- HERE I TRY TO FIND THE SELECTED CHECKBOXES AND CHECK THEM OFF -->
    if (isset($_GET['p_am'])) {
      $ams = $_GET['p_am'];

      echo '<div class="checkbox"><input type="checkbox" name="p_am" ' . $check . ' class="styled" value ="' . $properties_amenities . '"><label for="' . $am_name . '">' . $properties_amenities . '</label></div>';
    } else {
      echo '<div class="checkbox"><input type="checkbox" name="p_am" ' . $check . ' class="styled" value ="' . $properties_amenities . '"><label for="' . $am_name . '">' . $properties_amenities . '</label></div>';
    }
<!-- END ISSET -->

  }
} else {
  _e('There is no Properties Amenities', 'framework');
}
?>

For the multi select drop down I am using bootstrap multiselect, so on my template the code looks like this --

<select name="property_type[]" id="pt-multi" class="form-control multi-select2" multiple="multiple">
<?php
$terms = get_terms( "property-type", array( 'hide_empty' => 0 ) );
 $count = count($terms);
 if ( $count > 0  ){
echo "<option value='Any'>All</option>";
     foreach ( $terms as $term ) {
         echo "<option value='" . $term->slug . "'>" . $term->name . "</option>";
     }
 }
?>
</select>

On the page it renders out as ---

<select name="property_type[]" id="pt-multi" class="form-control multi-select2 iOSselect" multiple="multiple" style="display: none;">
<option value="Any">All</option>
<option value="co-op">Co-Op</option>
<option value="condo">Condo</option>
</select>

<div class="btn-group" style="width: 100%;">
<button type="button" class="multiselect dropdown-toggle btn btn-default form-control multi-select2" data-toggle="dropdown" title="Property Type" style="width: 100%; overflow: hidden; text-overflow: ellipsis;">
<span class="multiselect-selected-text">Property Type</span> 
<b class="caret"></b></button>
<ul class="multiselect-container dropdown-menu pull-right">
<li class="multiselect-item multiselect-all">
<a tabindex="0" class="multiselect-all">
<label class="checkbox"><input type="checkbox" value="multiselect-all">  Select all</label>
</a></li>
<li>
<a tabindex="0"><label class="checkbox">
<input type="checkbox" value="Any"> All</label>
</a></li>
<li>
<a tabindex="0"><label class="checkbox"><input type="checkbox" value="co-op"> Co-Op</label>
</a>
</li>
<li>
<a tabindex="0"><label class="checkbox"><input type="checkbox" value="condo"> Condo</label>
</a>
</li>
</ul>
</div>

Any ideas?