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Published online by Cambridge University Press: 12 March 2014
The two following papers are in need of certain corrections: Modal functions in two-valued logic and Note on modal functions. I became aware of the need for these corrections while comparing these earlier papers of mine with J. C. C. McKinsey's paper, On the syntactical construction of systems of modal logic.
The first of the two papers should be corrected in such a way that the system of two-valued logic there employed becomes “complete” in the sense that either p or ∼ p is in Τ for every Κ-symbol Τ. This could be achieved by use of an additional axiom that postulates the required completeness. (I mistakenly supposed that the original set of axioms guaranteed this completeness.)
1 This Journal, vol. 2 (1937), pp. 125–128.
2 Ibid., vol. 4 (1939), pp. 115–116.
3 Ibid., vol. 10 (1945), pp. 83–94.
4 Ibid., vol. 3 (1938), pp. 140–149.
5 See Theorem A of Note on modal functions.
6 This Journal, vol. 5 (1940), p. 31, last paragraph of the review.
7 See Carnap, R., Introduction to semantics. Harvard University Press, Cambridge, Mass., 1942, especially pp. 101–105.Google Scholar