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Transactions of the American Mathematical Society

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The undecidability of the word problems for projective geometries and modular lattices

Author: L. Lipshitz
Journal: Trans. Amer. Math. Soc. 193 (1974), 171-180
MSC: Primary 06A30; Secondary 02F47
MathSciNet review: 0364040
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Abstract: We show that the restricted word problems for finite-dimensional projective geometries and finite modular lattices and the word problem for modular lattices are undecidable.

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  • [1] Martin Davis, Computability and unsolvability, McGraw-Hill Series in Information Processing and Computers, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1958. MR 0124208
  • [2] Ju. L. Eršov, Decidability of the elementary theory of relatively complemented lattices and of the theory of filters, Algebra i Logika Sem. 3 (1964), no. 3, 17–38 (Russian). MR 0180490
  • [3] Ju. Š. Gurevič, The problem of equality of words for certain classes of semigroups, Algebra i Logika Sem. 5 (1966), no. 5, 25–35 (Russian). MR 0206079
  • [4] Robin Hartshorne, Foundations of projective geometry, Lecture Notes, Harvard University, vol. 1966/67, W. A. Benjamin, Inc., New York, 1967. MR 0222751
  • [5] Joachim Lambek, Lectures on rings and modules, With an appendix by Ian G. Connell, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1966. MR 0206032
  • [6] J. C. C. McKinsey, The decision problem for some classes of sentences without quantifiers, J. Symbolic Logic 8 (1943), 61–76. MR 0008991
  • [7] D. Scott, Convergent sequences of complete theories, Ph.D. Thesis, Princeton University, Princeton, N. J., 1958.
  • [8] Joseph R. Shoenfield, Mathematical logic, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1967. MR 0225631
  • [9] Philip M. Whitman, Free lattices, Ann. of Math. (2) 42 (1941), 325–330. MR 0003614
  • [10] John von Neumann, Continuous geometry, Foreword by Israel Halperin. Princeton Mathematical Series, No. 25, Princeton University Press, Princeton, N.J., 1960. MR 0120174

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Keywords: Undecidable word problems, projective geometry, modular lattices
Article copyright: © Copyright 1974 American Mathematical Society