Skip to main content

Linear lattice proof theory: An overview

Part of the Lecture Notes in Mathematics book series (LNM,volume 1149)

Keywords

  • Plane Graph
  • Projective Geometry
  • Congruence Lattice
  • Proof Theory
  • Modular Lattice

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. B. Artmann, “On coordinates in modular lattices.” Illinois J. Math. 12 (1968) 626–648.

    MathSciNet  MATH  Google Scholar 

  2. G. Birkhoff, Lattice Theory, Third Edition. AMS Colloquium Publications XXV, Providence RI (1967).

    MATH  Google Scholar 

  3. T. Brylawski, “A combinatorial model for series-parallel networks.” AMS Transactions 154 (1967) 1–22.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. P. Crawley and R. P. Dilworth, Algebraic Theory of Lattices. Prentice-Hall, Englewood Cliffs NJ (1973).

    MATH  Google Scholar 

  5. G. Czedli, “On lattice word problems with the help of graphs.” Preprint, Szeged (1982).

    Google Scholar 

  6. A. Day, “Geometrical applications in modular lattices.” Universal Algebra and Lattice Theory (Puebla, 1982), Springer-Verlag Lecture Notes in Mathematics 1004 (1983) 111–141.

    Google Scholar 

  7. A. Day and D. Pickering, “The coordinatization of Arguesian lattices.” AMS Transactions 278 (1983) 507–522.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. R. J. Duffin, “Topology of series-parallel networks.” J. Math. Analysis and Applications 10 (1965) 303–318.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. R. Freese, “Free modular lattices.” AMS Transactions 261 (1980) 81–91.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. G. Grätzer, General Lattice Theory. Birkhauser-Verlag, Basel (1978).

    CrossRef  MATH  Google Scholar 

  11. _____, Universal Algebra, Second Edition. Springer-Verlag, New York NY (1979).

    MATH  Google Scholar 

  12. M. Haiman, “The theory of linear lattices.” Ph.D. thesis, M. I. T. (1984).

    Google Scholar 

  13. _____, “Proof theory for linear lattices.” Advances in Math., to appear (1985).

    Google Scholar 

  14. Ch. Herrmann, “On the work problem for the modular lattice with four free generators.” Math. Annalen 265 (1983) 513–527.

    CrossRef  MATH  Google Scholar 

  15. W. Hodge and D. Pedoe, Methods of Algebraic Geometry, Volumes I, II, III. Cambridge Univ. Press, Cambridge (1953).

    MATH  Google Scholar 

  16. G. Hutchinson, “Recursively unsolvable word problems of modular lattices and diagram chasing.” J. Algebra 26 (1973) 385–399.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. _____, “A complete logic for n-permutable congruence lattices.” Alg. Universalis 13 (1981) 206–224.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. B. Jónsson, “On the representation of lattices.” Math. Scand. 1 (1953) 193–206.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. _____, “Modular lattices and Desargues’ theorem.” Math. Scand. 2 (1954) 295–314.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. _____, “Arguesian lattices of dimension n≤4.” Math. Scand. 7 (1959) 133–145.

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. _____, “Representation of modular lattices and of relation algebras.” AMS Transactions 92 (1959) 449–464.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. _____, “The class of Arguesian lattices is self-dual.” Alg. Universalis 2 (1972) 396.

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. B. Jónsson and G. S. Monk, “Representations of primary Arguesian lattices.” Pacific J. Math. 30 (1969) 95–139.

    CrossRef  MathSciNet  MATH  Google Scholar 

  24. L. Lipshitz, “The undecidability of the word problems of modular lattices and projective geometries.” AMS Transactions 193 (1974) 171–180.

    CrossRef  MathSciNet  MATH  Google Scholar 

  25. A. I. Mal’cev, “On the general theory of algebraic systems.” Mat. Sbornik (NS) 35, no. 7 (1954) 3–20. In Russian.

    MathSciNet  Google Scholar 

  26. O. Öre, “Theory of equivalence relations.” Duke Math. J. 9 (1942) 573–627.

    CrossRef  MathSciNet  MATH  Google Scholar 

  27. J. D. H. Smith, “Mal’cev varieties.” Springer-Verlag Lecture Notes in Mathematics 554, Berlin-Heidelberg (1976).

    Google Scholar 

  28. R. Smullyan, First Order Logic. Springer-Verlag, Berlin-Heidelberg (1968).

    CrossRef  MATH  Google Scholar 

  29. J. Von Neumann, Continuous Geometries. Princeton Univ. Press, Princeton NJ (1960).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1985 Springer-Verlag

About this paper

Cite this paper

Haiman, M. (1985). Linear lattice proof theory: An overview. In: Comer, S.D. (eds) Universal Algebra and Lattice Theory. Lecture Notes in Mathematics, vol 1149. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098460

Download citation

  • DOI: https://doi.org/10.1007/BFb0098460

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15691-8

  • Online ISBN: 978-3-540-39638-3

  • eBook Packages: Springer Book Archive