Transfinite Iteration Functionals and Ordinal Arithmetic
نویسنده
چکیده
Although transfinite iteration functionals have been used in the past to construct ever-larger initial segments of the ordinals ([5],[1]), there appears to be little investigation into the nature of the functionals themselves. In this note, we investigate the relationship between (countable) transfinite iteration and ordinal arithmetic. While there is a nice connection between finite iteration and addition, multiplication, and exponentiation, we show that this it is lost when passing to the transfinite and investigate a new equivalence relation on ordinal functionals with respect to which we restore it.
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