Is there a way to set a session by clicking a text?

I’m just curious. Is it possible to have a page where I list, let’s say, three links.

When the page is loaded first time the session is set to A.
And when the user is clicking on VERSION B, I would like the page to reload and set the session to B.
If they click on C it will be set to C.
Is this possible by just clicking a text link and not set the code in the url?
I kinda like when everything is happening in the background.

Or any other ideas on how to do this?

Well you could do it using javascript to submit a form, or use some CSS to make a button look like a link which would submit a form, which would at least hide the variable from the URL (though, any cursory glance at the page source would reveal you doing this)…

Can I have more than one button in one form? Or do you suggest making a different form for every link?

The latter. Form, Hidden Input (to transmit the data), Button, Close Form.