Thanks to all for the help. I will do some experiments. What I need is a combobox as defined in Wikipedia.
The desired behavior is the following. When I type characters in the edit, if there are matches, even partial, the list goes down and shows the items that match. If there are no matches, the list disappears. All dynamically as you type, as it happens, for example, when we type in the address bar of a browser. Nothing special. I'm probably wrong about setting some properties... but I can't get exactly that.