ยง 8102. Limitation of costs where action brought in higher court. A plaintiff is not entitled to costs: 1. in an action brought in the supreme court in a county within the city of New York which could have been brought, except for the amount claimed, in the civil court of the city of New York, unless he shall recover six thousand dollars or more; or, 2. in an action brought in the supreme court in a county not within the city of New York which could have been brought, except for the amount claimed, in any court of limited monetary jurisdiction in the county, unless he shall recover five hundred dollars or more; or, 3. in an action brought in the county court which could have been brought, except for the amount claimed, in any court of lesser monetary jurisdiction in the county, unless he shall recover two hundred fifty dollars or more.