This is the 32nd in a series of self contained postings to fom covering a wide range of topics in f.o.m. This posting concerns the greedy construction independence results. The last posting on this was 30. This obsoletes 30.
Analogous results hold starting from a given graph.
We now present an independence result about infinite construction sequences. In fact, we can require that they appear as new vertices in terms with isomorphic new parts. Here isomorphisms between graphs are order preserving bijections between the underlying integers which preserve the relevant structure. In fact, we can require that they appear as new vertices in terms with isomorphic new parts. This should be equivalent to the 1-consistency of type theory, or Zermelo set theory with bounded separation.