A. Troelstra, D. van Dalen, Constructivism in Mathematics, Vol 1, Ch. 3, Section 2, 1988, 120 (PRA na baze beskvantornoi (propozitsionalnoi) logiki, blizko k lektsii)
C. Smoryński, Modal Logic and Self-Reference, 1985 (PRA na baze logiki pervogo poryadka. (Smorinskii dopuskaet skhemu induktsii dlya $\Sigma_1$-formul, otozhdestvlyaya PRA i I $\Sigma_1$, no osnovnoe razvitie prokhodit i dlya beskvantornoi skhemy induktsii))
R. L. Goodstein, “Logic-free formalizations of recursive arithmetic”, Math. Scandinavica, 1954, № 2, 247–261 (Ekvatsionalnaya formulirovka PRA i (fakticheski) interpretatsiya v nei beskvantornoi PRA)
