No it does not imply constancy or consistency over time because the 4 axioms do not stop us from adding to the utility function a real-valued argument that represent the moment in time that the definition refers to.
In other words, the 4 axioms do not constrain us to consider only utility functions over world states: utility functions over “histories” are also allowed, where a “history” is a sequence of world states evolving over time (or equivalently a function that takes a number representing an instant in time and returning a world state).
No it does not imply constancy or consistency over time because the 4 axioms do not stop us from adding to the utility function a real-valued argument that represent the moment in time that the definition refers to.
In other words, the 4 axioms do not constrain us to consider only utility functions over world states: utility functions over “histories” are also allowed, where a “history” is a sequence of world states evolving over time (or equivalently a function that takes a number representing an instant in time and returning a world state).