## Fragments of many-valued statement calculi.(English)Zbl 0085.24303

### Keywords:

philosophy and foundations of mathematics
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 [1] Jan Łukasiewicz and Alfred Tarski, Untersuchungen über den Aussagenkalkül, Comptes Rendus des Séances de la Société des Sciences et des Lettres de Varsovie. Classe III vol. 23 (1930) pp. 30-50. · JFM 57.1319.01 [2] Emil L. Post, Introduction to a General Theory of Elementary Propositions, Amer. J. Math. 43 (1921), no. 3, 163 – 185. · JFM 48.1122.01 [3] Robert McNaughton, A theorem about infinite-valued sentential logic, J. Symbolic Logic 16 (1951), 1 – 13. · Zbl 0043.00901 [4] J. Barkley Rosser and Atwell R. Turquette, Many-valued logics, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Co., Amsterdam, 1951. · Zbl 0047.01503 [5] D. Hilbert and W. Ackermann, Grundzüge der Theoretischen Logik, 2d ed., Berlin, Springer, 1938. · JFM 64.0026.05 [6] T. Motzkin, Beiträge zur Theorie der Linear Ungleichungen, Doctoral dissertation, University of Basel, 1933 (Jerusalem, Azriel Printers, 1936). An English translation of this, under the title The theory of linear inequalities and with the reference number T-22, was published on March 7, 1952 by the RAND Corp., Santa Monica, California. [7] Alan Rose, The degree of completeness of the ℵ$$_{0}$$-valued Łukasiewicz propositional calculus, J. London Math. Soc. 28 (1953), 176 – 184. · Zbl 0053.20002 [8] M. Wajsberg, Beiträge zum Metaaussagenkalkül I, Monatsh. Math. Phys. 42 (1935), no. 1, 221 – 242 (German). · JFM 61.0972.01 [9] Alfred Tarski, Logic, semantics, metamathematics. Papers from 1923 to 1938, Oxford at the Clarendon Press, 1956. Translated by J. H. Woodger. · Zbl 0075.00702
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