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15
votes
Order type of the smallest set containing the identity function and closed under exponentiation
This is a partial answer, and I am unsure about part of it.
I claim that these functions are well-ordered by eventual
domination, and the order type is at most the ordinal $\epsilon_0$.
First, your …
1
vote
Rational exponential expressions
I don't have an answer to the one-variable decision
question that you asked.
But you did introduce multi-variable
expressions, and there are some fascinating results on the
multi-variable analogue of …