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).
Complete is also in question for any real-world application, because it implies consistent-over-time.
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).
Indeed there are quite a few interesting reasons to be skeptical of the completeness axiom.