Correct. Nor does “There is no time of death” refer to a set. You can model it as quantifying over a “set of times” if you like, just as Peano arithmetic can be modeled as quantifying over a “set of numbers”, but this does not mean the theory refers to sets, or infinity.
No, I mean that there are no infinite sets in first-order Peano arithmetic. The class “natural number” is not an object in Peano arithmetic.
First-order Peano arithmetic does not explicitly refer to sets, infinite sets, or natural numbers, but it describes them.
Correct. Nor does “There is no time of death” refer to a set. You can model it as quantifying over a “set of times” if you like, just as Peano arithmetic can be modeled as quantifying over a “set of numbers”, but this does not mean the theory refers to sets, or infinity.