The problem needs lots of little hypotheses about Omega. In general, you can create these hypotheses for yourself, using the principle of "Least Convenient Possible World"

http://lesswrong.com/lw/2k/the_least_convenient_possible_world/

Or, from philosophy/argumentation theory, "Principle of Charity".

http://philosophy.lander.edu/intro/charity.shtml

In your case, I think you need to add at least two helper assumptions - Omega's prediction abilities are trustworthy, and Omega's offer will never be repeated - not for you, not for anyone.