So it looks very much as though Arsenal will be in the Champions League next season
if UEFA are unable to finish the Champions League and Europa Leagues with all of Europe's top leagues having to finish in a tight window and/or we are unable to complete the Premier League season. This is due to Arsenal having the 4th highest UEFA co-efficient - largely based on the success under Arsene Wenger.
This means that Man City, Liverpool, Manchester United & Arsenal will be the PL's representatives in next season's competition. Unfortunately for Tottenham; they would miss out.