A free IPC is a natural logic: Strong completeness for some intuitionistic free logics

Axcel, P., ≪Saturated intuitionistic theories≫, in Contributions to Mathematical Logic (Schmidt, Schütte and Thiele, eds.) North Holland, 1968, pages 1–11. Bencivenga, E., ≪Free semantics≫, Boston Studies in the Philosophy of Science, 47, 1980, pages 31–48. Brouwer, L.E.J., ≪Intuitionistische Zerlegung mathematischen Grundbegriffe≫, Jber. Deutsch. Math. Verein. 33, 1924, pages 251–256. ([6], pages 275–280). Brouwer, L.E.J., Über Definitionsbereich e von Funktionen≫, Math. Annalen, 97, pages 60–75. ([6], pages 390–405). Brouwer, L.E.J., ≪Willen, weten, spreken≫ Euclides, Groningen, 9, pages 177–193. (Translated in [6], pages 443–446). Brouwer, L.E.J., Collected Works, v.1., (A. Heyting, ed.), North Holland, 1975. Burge, T., ≪Truth and singular terms.≫, Nous, VIII, 1974, pages 309–325. Cocchiarella, N., ≪On the primary and secondary semantics of logical necessity≫, JPL, 4, 1975, pages 13–28. Grandy, R., ≪Predication and singular terms≫, Nous, XI, 1977, pages 163–167. Heyting, A., ≪Die formalen Regeln der intuitionistischen Logik≫, Sitzungsber. preuss. Akad. Wiss., 1930, pages 42–56. Hintikka, J., Logic, Language Games and Information, Oxford University Press, 1973. Kleene, S.C., ≪Disjunction and existence under implication in elementary intuitionistic formalisms≫, JSL, 27, 1962, pages 11–18. Kleene, S.C., and Vesley, R., Foundations of Intuitionistic Mathematics, North Holland, 1965. Kripke, S., ≪Semantical analysis of intuitionistic logic, I,≫ in Formal Systems and Recursive Functions, (Crossley and Dummett, eds.), North Holland, 1965, pages 92–130. Lambert, K., ≪Notes on E!, III: A theory of descriptions≫, Phil. Studies, 13, 1962, pages 51–59. Leblanc, H., and Gumb, R., ≪Soundness and completeness proof for three brands of Intuitionistic logic≫, in Essays in Epistemology and Semantics, (Leblanc, Gumb and Stern, eds.), Haven, forthcoming. Leblanc, H., and Thomason, R., ≪Completeness theorems for some presupposition-free logics≫, Fundamenta Mathematicae, 62, 1968, pages 125–164. Myhill, J., ≪Formal systems of intuitionistic analysis, I≫, in Logic Methodology and Philosophy of Science, III, (van Rootselaar and Staal, eds.), North Holland, 1968, pages 161–178. Posy, C., ≪Brouwer's constructivism≫, Synthese, 27, 1974, pages 125–159. Robinson, T., ≪Interpretations of Kleene's metamathematical predicate in intuitionistic arithmetic≫, JSL, 30, 1965, pages 140–154. Schock, R., Logics without Existence Assumptions, Almqvist & Wiksell, (Stockholm), 1968. Smorynski, C., ≪Applications of Kripke models≫, in Metamathematical Investigations of Intuitionistic Arithmetic and Analysis, (A.S. Troelstra, ed.), Springer (L.N.M. 344), 1973, pages 324–391. Stenlund, S., ≪Descriptions in intuitionistic logic≫, in Proc. Third Scand. Logic Symp., (S. Kanger, ed.), North Holland, 1975, pages 197–212. Thomason, R., ≪On the strong semantical completeness of the intuitionistic predicate calculus≫, JSL, 33, 1965, pages 1–7. Troelstra, A., ≪Intuitionistic formal systems≫, in Metamathematical Investigations of Intuitionistic Arithmetic and Analysis, (A. Troelstra, ed.) Springer (L.N.M. 344), 1973, pages 1–96. Van Fraassen, B., ≪The completeness of free logic≫, Zeitschrift für math. Logik und Grundlagen der Math., 12, 1966, pages 219–234. Van Fraassen, B., ≪Singular terms, truth-value gaps, and free logic≫, J. Phil., 67, 1966, pages 481–495.