Ramified theory of types

See impredicative definition, and paradoxes, logical.

B. Russell,

Mathematical logic as based on the theory of types, American Journal of Mathematics, vol. 30 (1908), pp. 222- 262.

L. Chwistek,

The theory of constructive types, Annales de la Societe Polonaise de Mathematique, vol. 2 (1924), pp. 9-48, and vol. 3 (1925), pp. 92-141.

W. V. Quine,

On the axiom of reducibthty, Mind, n. s. vol. 45 (1936), pp. 498-500.

F. B. Fitch,

The consistency of the ramified Principia, The Journal of Symbolic Logic, vol. 3 (1938), pp. 140-149.