In recent years, this has advanced to a study of Boolean relation theory, which attempts to justify large cardinal axioms by demonstrating their necessity for deriving certain propositions considered "concrete".

Friedman earned his Ph.D. from the Massachusetts Institute of Technology in 1967, at age 19, with a dissertation on Subsystems of Analysis.

[7] Jordana Cepelewicz (2017) profiled Friedman in Nautilus as "The Man Who Wants to Rescue Infinity".

[9] In this manuscript, Friedman showed how, starting from the hypothesis of the existence of God (in the sense of Gödel's ontological proof), it can be shown that mathematics, as formalized by the usual ZFC axioms, is consistent.

[10] He invented and proved important theorems regarding the finite promise games and greedy clique sequences, and Friedman's grand conjecture bears his name.