Via the use of results from approximation theory to indicate the flexibility available in particular models of set theory in choosing entire functions of one variable which are order-isomorphisms of everywhere nonmeager subsets of R of cardinality ℵ1, or entire functions of n variables which are large cross-sections through everywhere nonmeager subsets of Rn+1, new variations on the results from approximation theory have arisen. We survey this interplay between the two topics.