Linked bibliography for the SEP article "The Algebra of Logic Tradition" by Stanley Burris |
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- Boole, G., 1847, The Mathematical Analysis of Logic, Being an Essay Towards a Calculus of Deductive Reasoning, Cambridge: Macmillan, Barclay, & Macmillan; reprinted Oxford: Basil Blackwell 1951. (Scholar)
- –––, 1854, An Investigation of The Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities , London: Macmillan; reprint by Dover 1958. (Scholar)
- Dedekind, R., 1897, “Über Zerlegungen von Zahlen durch ihre grössten gemeinsamen Teiler,” reprinted in Gesammelte mathematische Werke (1930–1932), 2: 103–147. (Scholar)
- –––, 1930–1932, Gesammelte mathematische Werke, Robert Fricke, Emmy Noether, Öystein Ore (eds.), Braunschweig: Friedr. Vieweg & Sohn. (Scholar)
- De Morgan, A., 1847, Formal Logic: or, the Calculus of Inference, Necessary and Probable, London: Taylor and Walton; reprinted London: The Open Court Company 1926. (Scholar)
- –––, 1966, On the Syllogism, and Other Logical Writings, a posthumous collection of De Morgan's papers on logic, ed. Peter Heath, New Haven, Yale University Press. (Scholar)
- Feferman, S., and Vaught, R. L., 1979, “The first order properties of products of algebraic systems,” Fundamenta Mathematica, 47: 57–103. (Scholar)
- Frege, F., 1879, Begriffsschrift: eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Halle a. S.: Louis Nebert. (Scholar)
- –––, 1884, Die Grundlagen der Arithmetik:eine logisch-mathematische Untersuchung über den Begriff der Zahl, Breslau: W. Koebner. (Scholar)
- –––, 1893/1903, Grundgesetze der Arithmetik, begriffsschriftlich abgeleitet, 2 vols, Jena: Verlag Hermann Pohle. (Scholar)
- Halmos, P.R., 1956, “Algebraic logic. I. Monadic Boolean algebras,” Compositio Mathematica, 12: 217–249. (Scholar)
- –––, 1956, “The basic concepts of algebraic logic,” American Mathematical Monthly, 63: 363–387. (Scholar)
- –––, 1956, “Algebraic logic. II. Homogeneous locally finite polyadic Boolean algebras of infinite degree,” Fundamenta Mathematica, 43: 255–325. (Scholar)
- –––, 1956, “Algebraic logic. III. Predicates, terms, and operations in polyadic algebras,” Transactions of the American Mathematical Society, 83: 430–470. (Scholar)
- –––, 1957, “Algebraic logic. IV. Equality in polyadic algebras,” Transactions of the American Mathematical Society, 86: 1–27. (Scholar)
- –––, 1962, Algebraic logic, New York: Chelsea Publishing Co. (Scholar)
- Henkin, L., and Monk, J. D., 1974, “Cylindric algebras and related structures,” in L. Henkin et al. (eds.), Proceedings of the Tarski Symposium, Proceedings of Symposia in Pure Mathematics, vol. XXV, Providence, RI: American Mathematical Society, pp. 105–121. (Scholar)
- Henkin, L, and Tarski, A., 1961, “Cylindric algebras,” in: Lattice Theory, Proceedings of Symposia in Pure Mathematics 2, R. P. Dilworth (ed.), Providence, RI: American Mathematical Society, pp. 83–113. (Scholar)
- Hilbert, D., 1899, The Foundations of Geometry; reprinted Chicago: Open Court 1980, 2nd edition. (Scholar)
- –––, D. and Ackermann, W., 1928, Grundzüge der theoretischen Logik, Berlin: Springer. (Scholar)
- Huntington, E. V., 1904, “Sets of independent postulates for the algebra of logic,” Transactions of the American Mathematical Society, 5: 288–309. (Scholar)
- –––, 1933, “New sets of independent postulates for the algebra of logic, with special reference to Whitehead and Russell's Principia Mathematica,” Transactions of the American Mathematical Society, 35(1): 274–304. (Scholar)
- Jevons, W. S., 1869, The Substitution of Similars, the True Principle of Reasoning, Derived from a Modification of Aristotle's Dictum, London: Macmillan and Co. (Scholar)
- –––, 1870, Elementary Lessons in Logic, Deductive and Inductive, London: Macmillan & Co.; reprinted 1957. (Scholar)
- –––, 1874, The Principles of Science, A Treatise on Logic and the Scientific Method, London and New York: Macmillan and Co.; reprinted 1892. (Scholar)
- –––, 1880, Studies in Deductive Logic. A Manual for Students, London and New York: Macmillan and Co. (Scholar)
- –––, 1883, The Elements of Logic, New York and Chicago: Sheldon & Co. (Scholar)
- –––, 1890, Pure Logic and Other Minor Works, Robert Adamson and Harriet A. Jevons (eds), New York: Lennox Hill Pub. & Dist. Co.; reprinted 1971. (Scholar)
- Jónsson, B., and Tarski, A., 1951, “Boolean Algebras with Operators. Part I,” American Journal of Mathematics, 73(4): 891–939. (Scholar)
- Löwenheim, L., 1915, “Über möglichkeiten im Relativkalül,” Mathematische Annalen, 76(4): 447–470. (Scholar)
- Mostowski, A., 1952, “On direct products of theories,” Journal of Symbolic Logic, 17: 1–31. (Scholar)
- Peirce, C. S., 1870, “Description of a notation for the logic of relatives, resulting from an amplification of the conceptions of Boole's calculus of logic,” Memoirs of the American Academy, 9: 317–378; reprinted in Vol. III of Collected Papers, 27–98. (Scholar)
- –––, 1880, “On the algebra of logic. Chapter I: Syllogistic. Chapter II: The logic of non-relative terms. Chapter III: The logic of relatives,” American Journal of Mathematics, 3: 15–57; reprinted in Collected Papers (1933), Volume III, 104–157. (Scholar)
- –––, 1885, “On the Algebra of Logic; A Contribution to the Philosophy of Notation,” American Journal of Mathematics 7: 180–202; reprinted in Collected Papers (1933). (Scholar)
- –––, 1933, Collected Papers, Charles Hartshorne and Paul Weiss (eds.), Cambridge: Harvard University Press. (Scholar)
- Schröder, E., 1890–1910, Algebra der Logik, Vols. I–III; reprint Chelsea 1966. (Scholar)
- Sheffer, H. M., 1913, “A set of five independent postulates for Boolean algebras, with application to logical constants,” Transactions of the American Mathematical Society, 14(4): 481–488. (Scholar)
- Skolem, T., 1919, “Untersuchungen über die Axiome des Klassenkalküls und Über Produktations- und Summationsprobleme, welche gewisse Klassen von Aussagen betreffen,” Videnskapsselskapets skrifter, I. Matematisk-naturvidenskabelig, klasse 3; reprinted in Skolem (1970, 66–101). (Scholar)
- –––, 1920, “Logisch-kombinatorische Untersuchungen über die Erfülbarkeit oder Beweisbarkeit mathematischer Sätze nebst einem Theoreme über dichte Menge,” Videnskapsselskapets skrifter, I. Matematisk-naturvidenskabelig, klasse 6: 1–36. (Scholar)
- –––, 1922, “Einige Bemerkungen zur axiomatischen Begrundung der Mengenlehre,” Matematikerkongressen i Helsingfors den 4–7 Juli 1922, Den femte skandinaviska matematikerkongressen, Redogörelse, Heskinki: Akademiska Bokhandeln; reprinted in Skolem (1970, 189–206). (Scholar)
- –––, 1928, “Über die mathematische Logik,” Norsk Mathematisk Tidsskrift, 10: 125–142; in van Heijenoort (1967), 508–524. (Scholar)
- –––, 1970, Selected Works in Logic, Oslo: Universitetsforlaget. (Scholar)
- Stone, M. H., 1936, “The theory of representations for Boolean algebras,” Transactions of the American Mathematical Society, 40(1): 37–111. (Scholar)
- –––, 1937, “Applications of the theory of Boolean rings to general topology,” Transactions of the American Mathematical Society, 41(3): 375–481. (Scholar)
- Tarski, A., 1941, “On the calculus of relations,” The Journal of Symbolic Logic, 6(3): 73–89 (Scholar)
- ––– and Givant, S., 1987, Set Theory Without Variables, (Series: Colloquium Publications, Volume 1), Providence: American Mathematical Society. (Scholar)
- Whitehead, A. N., and Russell, B., 1910–1913, Principia Mathematica I–III, Cambridge: Cambridge University Press. (Scholar)
- Whitman, P. M., 1941, “Free lattices,” Annals of Mathematics (2), 42: 325–330. (Scholar)
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