Rikkitic:
This generation already has trouble paying for things that will only benefit the next one. How the hell are they going to finance an intergenerational space ship?
It's unlikely that something like this would be publicly funded. I also didn't say it was likely, but it's technically conceivable solution to long interstellar flights.
Once we have people living and surviving in the solar system outside of earth, the construction possibilities change. There is abundant material for construction of space craft, abundant fuel and reasonably abundant ice. The possibilities are substantial at that point.
Impressive progress has been made on systems for food production and waste management.