Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Finite substructure lattices of models of Peano arithmetic


Author: James H. Schmerl
Journal: Proc. Amer. Math. Soc. 117 (1993), 833-838
MSC: Primary 03H15; Secondary 03C62, 06B15
DOI: https://doi.org/10.1090/S0002-9939-1993-1112501-8
MathSciNet review: 1112501
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Some new finite lattices (for example, $ {M_4},\;{M_7}$, and the hexagon lattice) are shown to be isomorphic to the lattice of elementary substructures of a model of Peano Arithmetic.


References [Enhancements On Off] (What's this?)

  • [1] W. Feit, An interval in the subgroup lattice of a finite group which is isomorphic to $ {M_7}$, Algebra Universalis 17 (1983), 220-221. MR 726276 (85d:20022)
  • [2] H. Gaifman, Models and types of Peano's arithmetic, Ann. Math. Logic 9 (1976), 223-306. MR 0406791 (53:10577)
  • [3] G. Grätzer and E. T. Schmidt, Characterizations of congruence lattices of abstract algebras, Acta. Sci. Math. (Szeged) 24 (1963), 34-39. MR 0151406 (27:1391)
  • [4] J. Paris, On models of arithmetic, Conference in Mathematical Logic, London '70, Lecture Notes in Math., vol. 225, Springer-Verlag, Heidelberg and New York, 1972, pp. 252-280. MR 0392552 (52:13369)
  • [5] -, Models of arithmetic and the $ 1$-$ 3$-$ 1$ lattice, Fund. Math. 95 (1977), 195-199. MR 0446953 (56:5270)
  • [6] H. J. Prömel and B. Voigt, Canonical partition theorems for parameter sets, J. Combin. Theory (A) 35 (1983), 309-327. MR 721372 (85i:05171)
  • [7] J. H. Schmerl, Extending models of arithmetic, Ann. Math. Logic 14 (1978), 89-109. MR 506527 (80f:03036)
  • [8] -, Substructure lattices of models of Peano Arithmetic, Logic Colloquium '84, North-Holland, Amsterdam, 1986, pp. 225-243. MR 861427 (87j:03046)
  • [9] A. Wilkie, On models of arithmetic having non-modular substructure lattices, Fund. Math. 95 (1977), 223-237. MR 0446952 (56:5269)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 03H15, 03C62, 06B15

Retrieve articles in all journals with MSC: 03H15, 03C62, 06B15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1112501-8
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society