jQuery Forum

By default, the jQuery UI tabs widget uses an unordered list to present its tabs.  When using tabs for a sites' main navigation, each tab represents a major section.  However, my understanding of proper semantic HTML--including how search engines give meaning to data--dictates that headings be used to denote major sections.

Is it possible and semantically valid to put headings within unordered list items?

E.g., with this basic HTML:

1. <h1 ><a href="homepage.htm">Website Title</a></h1>
   
   <div id="tabs">
       <ul>
           <li><a href="#fragment-1"><span>Tab 1</span></a></li>
           <li><a href="#fragment-2"><span>Tab 2</span></a></li>
           <li><a href="#fragment-3"><span>Tab 3</span></a></li>
       </ul>
       <div id="fragment-1">
           Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy nibh euismod         tincidunt ut laoreet dolore magna aliquam erat volutpat.
       </div>
       <div id="fragment-2">
          Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy nibh euismod         tincidunt ut laoreet dolore magna aliquam erat volutpat.
       </div>
       <div id="fragment-3">
           Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy nibh euismod         tincidunt ut laoreet dolore magna aliquam erat volutpat.
       </div>
   </div>
   
   </body>

Adding <h2> tags inside the <li>:

1. <h1 ><a href="homepage.htm">Website Title</a></h1>
   
   <div id="tabs">
       <ul>
           <li><h2><a href="#fragment-1"><span>Tab 1</span></a></h2></li>
           <li><h2><a href="#fragment-2"><span>Tab 2</span></a></h2></li>
           <li><h2><a href="#fragment-3"><span>Tab 3</span></a></h2></li>
       </ul>
       <div id="fragment-1">
           Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy nibh euismod         tincidunt ut laoreet dolore magna aliquam erat volutpat.
       </div>
       <div id="fragment-2">
          Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy nibh euismod         tincidunt ut laoreet dolore magna aliquam erat volutpat.
       </div>
       <div id="fragment-3">
           Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy nibh euismod         tincidunt ut laoreet dolore magna aliquam erat volutpat.
       </div>
   </div>

If so, why wouldn't you include them?  This assumes that the headings can styled with CSS to match the original look of the unordered list.