Decoherence on its own still has a basis problem. You need superselection to reduce that to one basis. However this has been shown long ago (1980s) so in essenc

Decoherence on its own still has a basis problem. You need superselection to reduce that to one basis. However this has been shown long ago (1980s) so in essence decoherence + superselection does solve these problems. If you're not familiar with these terms I can explain.