Hi again,
English grammar books published in Japan explains:
"This is the doll that he made yesterday," suggests that he made only one doll yesterday. Yes.
It also suggests that the listener is already aware that a doll was made.
You might like to consider these examples.
example 1.
I don't know you make dolls.
You walk into the room and say 'This is a doll that I made yesterday'.
I say 'Oh, how nice'.
example 2.
I don't know you make dolls.
You walk into the room and say 'This is the doll that I made yesterday'.
I say 'What doll? What are you talking about?'
"This is a doll that he made yesterday," suggests that he made more than one doll yesterday. I'd say it depends on the context.
Nevertheless, can I use "This is a doll that he made yesterday" in the following cases?
1. I do not know how many dolls he made yesterday (he might have made one doll or more than one doll). Yes
2. It does not look like a doll (because he is clumsy and the person I am talking to said, "What's this waste cloth?" In this case, it does not matter how many dolls he made yesterday.) Yes
Clive