The definition has changed over time, but you have reduced the definition to a single component. It is true that an element of the ethos is to improve the outcomes of your descendants. The American Dream can be reduced simply to mean America exists as a place where you can live a better life. This concept is predicated on the statement in the Declaration of Independence that "all men are created equal." We may agree that this statement was not enacted with sincerity, but we may hope that is will be.
Much of the world views the American Dream as America as a place where one can come, work hard, be treated fairly and be rewarded regardless of social class or circumstances of birth.
The extrapolation of this concept into a larger ethos that includes upward, inter-generational class mobility makes sense, but is just one element of an ethos based on the basic principles of "life, liberty and the pursuit of happiness."
Much of the world views the American Dream as America as a place where one can come, work hard, be treated fairly and be rewarded regardless of social class or circumstances of birth.
The extrapolation of this concept into a larger ethos that includes upward, inter-generational class mobility makes sense, but is just one element of an ethos based on the basic principles of "life, liberty and the pursuit of happiness."