Our omega-matic 4500 does not accept the universal wireless keyless entry HELP

SOURCE: programming my keyless entry

Yes, you purchased the wrong wireless. You must get a Genie keyless and there are two types of Genie keyless (GWKP & GWK-BL) depending on which Genie operator you have. You might think about a wired keyless entry (Domino GD-1). Then if you change your operator you don't have to change your keyless.