I am trying to find two predicates that don't work when the positions of different types of quantifiers are switched.
The first one is when:
∀x ∃ y P( x, y ) is true but ∃ y ∀ x P( x, y ) is false
So I though when you let P(x, y) denote x < y would satisfy that one. The second predicate I need is when:
∃ x ∀ y P( x, y ) is true but ∀y ∃ x P( x, y ) is false.
A simple answer to this would be preferable like my previous one.