Re: R.J. Lipton • Failure Of Unique Factorization
My favorite question in this realm is how much of the linear ordering of the natural numbers is purely combinatorial, where we eliminate all the structure that isn’t purely combinatorial via the doubly recursive factorizations of whole numbers, ending up with two species of graph-theoretic structures that I dubbed Riffs and Rotes. See the following links for more discussion:
Inquiry Into Inquiry 