If PM's ramified types can be reduced to simple types for most mathematical purposes—as Church and others argued—then the equiconsistency bridge to ZF is substantive, not merely formal.

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Church(in the history of logic and computation): Alonzo Church (1903-1995), an American logician and mathematician who created formal systems to define what problems can be solved by mathematical procedures.
Equiconsistency(describing the relationship between two formal systems): When two mathematical systems are equally safe from contradiction—if one has no hidden logical problems, neither does the other.
PM (Principia Mathematica)(the foundational system being discussed): A massive three-volume work published in the early 1900s by Bertrand Russell and Alfred North Whitehead that tried to build all of mathematics from basic logical rules.
Ramified types(a feature of Principia Mathematica): A complicated system Russell created to organize mathematical objects into layers to avoid logical contradictions, where higher layers are kept separate from lower ones.

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