1. Rudolf Carnap, Meaning and Necessity, University of Chicago Press, Chicago, Illinois, (1950), pp. 32–39.
2. H. Leblanc and R. K. Meyer, ‘On Prefacing (∀X) A→A(Y/X) with (∀X) — A Free Quantification Theory Without Identity’, Zeitschr. f. math. Logik und Grundlagen d. Math., 16, (1970), pp. 447–462. Typing limitations require a departure from some of their symbols, but the conventions and definitions of the proof theory remain the same.
3. See Bertrand Russell, ‘On Denoting’, Mind, XIV, (1905), pp. 479–493.
4. W. V. Quine, ‘New Foundations for Mathematical Logic’, American Mathematical Monthly 44, 1937, pp. 70–80.
5. See Karel Lambert, ‘A Theory of Definite Descriptions’ in Philosophical Applications of Free Logic (Ed. K. Lambert), Oxford, London, 1990. This essay is a fusion of two papers published in 1962 and 1964. See, also, Rolf Schock, Logics Without Existence Assumptions, Almqvist & Wiksells, Uppsala, 1968; David Kaplan, ‘What is Russell’s Theory of Descriptions?’ in Physics, Logic and History (Eds. W. Yourgrau et. al.), Plenum, New York, 1970; and Dana Scott, ‘Existence and Description in Formal Logic’, in Bertrand Russell: Philosopher of the Century (Ed. R. Schoenman), Allen & Unwin, London, 1967.