My feeling is that someone just "says" is because "other says". How to be sure someone is right, if he cannot show why is right (not speaking of you I'm in general sayings)?. Also your claim "to any set of E" is quite generic and assumes that you defined E as Richardson, if E in example is just a polynomial your claim do not hold anymore. People pretends me to be precise in the question, but then do generic answers without contextualization while it is obvious to everyone what I did not understand, no one cared to explain ^^.

That's because you know what the theorem is about, if you read it on Wikipedia it is not clear at all. Everyone is good to criticize and downvote when someone do not understand because someone else wrote that in a bad way. Math should not be elitarie in any way. Everyone here just sad "that's obvious", but math is not at all obviouse, you have to show it is obvious. Math is made by many steps, if it is not clear enough you should explain what is missing step. Not insisting in "it is that way." show that way ^^.

Now I understand but I think it is more clear in the following way: "Since expressions mentioned in Richardson theorem are a subset of mine expressions, then mine expressions have a subset for which some expressions are not decidable on the condition." No one still exclude then that expressions using at least one time the "square root" function may be trivially decidable then. About the usage of $|x|$ I still have some doubts but Thanks for the spotlight. ^^

I do not understan why, Richardson use "abs" and don't have "sqrt and pow" functions.. Maybe you can link the theorem in an answer @EmilJeřábek ? (at least according to wikipedia page) I'm not going to trust a theorem without explaination if I'm not working under the assumptions of the theorem

I edited to made it very formal so that everyone is happy and can understand now ^^