From the book by Marty Bergen (1985), Better Bidding with Bergen — Volume One, Uncontested Auctions.
4

says let’s play in a Part Score 4

or 4

4

is asking opener to bid a singleton: responses are
4

=

singleton, 4

=

singleton, 4NT=minor suit singleton, and 5

no singleton.
Depending on the location of the singleton and your hand, responder is usually interested in playing in a game, 5

or 5

or a slam, 6

or 6

.
Example: Responder has:

A K Q x

x x

A K Q x

x x x
With a heart singleton, you want to play in 6

otherwise you would bid 5

.
4

and 4

are signoffs in responders long suit. Opener must pass.
4NT is invitational to slam, asking opener to bid a minor suit slam with an extra trick.
Example: Responder has like

Q x x

x x

x

A K Q J x x x
5

asks opener to play in a game, either 5

or 5

.
5

is a signoff by responder, responder knows that the opener has long diamonds and wants to play game from his
side.
6

is to play slam in 6

or 6

, opener is to pick the suit.
Again, a bid of 6

by responder is to play slam in diamonds, responder knows that it is the long suit.
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