This article on Wizards of the Coast website claims that Eater of Days "lose your next two turns" can be avoided by use of Sundial of the Infinite. I can't figure that out. There are no rulings on Eater of Days, and it is not an "end of turn" type of effect. Is the author just wrong? [seems unlikely] Or maybe the rules have changed?
A ruling on Sundial of the Infinite says
Ending the turn this way means the following things happen in order: 1) All spells and abilities on the stack are exiled. This includes spells and abilities that can't be countered. 2) All attacking and blocking creatures are removed from combat. 3) State-based actions are checked. No player gets priority, and no triggered abilities are put onto the stack. 4) The current phase and/or step ends. The game skips straight to the cleanup step. The cleanup step happens in its entirety.
Eater of Days' ability is a triggered ability, so if you respond to it by activating Sundial of the Infinite, that triggered ability will be exiled and will never resolve. So, you don't have to skip any turns.
Yes, Sundial of the Infinite can be used to avoid skipping your next two turns. Here is what happens in more detail:
- You have Sundial of the Infinite on the board.
- You cast Eater of Days.
- Eater of Days enters the battlefield, and its triggered ability, "When Eater of Days enters the battlefield, you skip your next two turns." is put on the stack.
Note: triggered abilities are defined in detail in comprehensive rule 603.
- You activate Sundial of the Infinite's ability.
- Everyone passes priority. (i.e. it is possible for an opponent to respond to Sundial of the Infinite's activation)
- Step (1) of of Sundial of the Infinite's ability exiles "you skip your next two turns" from the stack.
Note: The details of how to resolve Sundial of the Infinite's ability is covered in comprehensive rule 713.
At present, three cards can stop a turn. Sundial of the Infinite, Time Stop and Obeka, Brute Chronologist. The rulings on those cards are consistent, but different, and it's worth reading all of them to understand the implications.