The structure of superilat graphs

A. Ivanov

Fundamenta Mathematicae (1993)

  • Volume: 143, Issue: 2, page 107-117
  • ISSN: 0016-2736

Abstract

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We prove a structure theorem asserting that each superflat graph is tree-decomposable in a very nice way. As a consequence we fully determine the spectrum functions of theories of superflat graphs.

How to cite

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Ivanov, A.. "The structure of superilat graphs." Fundamenta Mathematicae 143.2 (1993): 107-117. <http://eudml.org/doc/211995>.

@article{Ivanov1993,
abstract = {We prove a structure theorem asserting that each superflat graph is tree-decomposable in a very nice way. As a consequence we fully determine the spectrum functions of theories of superflat graphs.},
author = {Ivanov, A.},
journal = {Fundamenta Mathematicae},
keywords = {tree-decomposability; structure theorem; spectrum functions of theories of superflat graphs},
language = {eng},
number = {2},
pages = {107-117},
title = {The structure of superilat graphs},
url = {http://eudml.org/doc/211995},
volume = {143},
year = {1993},
}

TY - JOUR
AU - Ivanov, A.
TI - The structure of superilat graphs
JO - Fundamenta Mathematicae
PY - 1993
VL - 143
IS - 2
SP - 107
EP - 117
AB - We prove a structure theorem asserting that each superflat graph is tree-decomposable in a very nice way. As a consequence we fully determine the spectrum functions of theories of superflat graphs.
LA - eng
KW - tree-decomposability; structure theorem; spectrum functions of theories of superflat graphs
UR - http://eudml.org/doc/211995
ER -

References

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  2. [2] J. T. Baldwin and S. Shelah, Second-order quantifiers and the complexity of theories, Notre Dame J. Formal Logic 26 (1985), 229-303. Zbl0596.03033
  3. [3] H. Herre, A. H. Mekler and K. Smith, Superstable graphs, Fund. Math. 118 (1983), 75-79. Zbl0698.05042
  4. [4] E. Hrushovski, Unidimensional theories are superstable, Ann. Pure Appl. Logic 50 (1990), 117-138. Zbl0713.03015
  5. [5] L. F. Low, Superstable trivial theories, preprint. 
  6. [6] M. Makkai, A survey of basic stability theory, with particular emphasis on orthogonality and regular types, Israel J. Math. 49 (1984), 181-238. Zbl0583.03021
  7. [7] L. Marcus, The number of countable models of a theory of one unary function, Fund. Math. 108 (1980), 171-181. Zbl0363.02055
  8. [8] E. A. Palyutin and S. S. Starchenko, Horn theories with non-maximal spectra, in: Model Theory and its Applications, Yu. L. Ershov (ed.), Nauka, Novosibirsk, 1988, 108-161. Zbl0672.03020
  9. [9] A. Pillay, Simple superstable theories, in: Classification Theory, J. T. Baldwin (ed.), Lecture Notes in Math. 1292, Springer, Heidelberg, 1987, 247-263. 
  10. [10] K. Podewski and M. Ziegler, Stable graphs, Fund. Math. 100 (1978), 101-107. Zbl0407.05072
  11. [11] A. N. Ryaskin, The number of models of complete theories of unars, in: Model Theory and its Applications, Yu. L. Ershov (ed.), Nauka, Novosibirsk, 1988, 162-182 (in Russian). Zbl0924.03062
  12. [12] J. Saffe, The number of uncountable models of ω-stable theories, Ann. Pure Appl. Logic 24 (1983), 231-261. Zbl0518.03010
  13. [13] S. Shelah, Classification Theory and the Number of Non-Isomorphic Models, North-Holland, Amsterdam, 1978. Zbl0388.03009
  14. [14] S. Shelah, On almost categorical theories, in: Classification Theory, J. T. Baldwin (ed.), Lecture Notes in Math. 1292, Springer, Heidelberg, 1987, 498-500. 

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