Quick filtering concept

gistfile1.phtml

<?php
	$searcharg = array();
	global $searcharg;
	
	add_action( 'init', 'check_form' );
	add_action( 'pre_get_posts', 'make_fancy_query' );
	
	function check_form() {
		if ( isset( $_GET['Checkme'] ) ) {
			global $searcharg;
			$searcharg = $_GET['Checkme'];
		}
	}
	
	function make_fancy_query( $query ) {
		global $searcharg;
		if ( $query->is_main_query() && ! empty( $searcharg ) ) {
			$query->set();
		}
	}
?>



<form action="" method="get">
	<input type="text" name="s">
	
	<input type="checkbox" name="Checkme" value="check1">
	<input type="checkbox" name="Checkme" value="check2">
	<input type="checkbox" name="Checkme" value="check3">
	
	<input type="submit" value="Search">