Pacific Journal of Mathematics

A combinatorial problem; stability and order for models and theories in infinitary languages.

Saharon Shelah

Article information

Pacific J. Math., Volume 41, Number 1 (1972), 247-261.

First available in Project Euclid: 13 December 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 02H10
Secondary: 02B25 04A20 05A05: Permutations, words, matrices


Shelah, Saharon. A combinatorial problem; stability and order for models and theories in infinitary languages. Pacific J. Math. 41 (1972), no. 1, 247--261.

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  • [1] C.C.Chang, Some remarks onthemodel theory of infinitarylanguages, Lecture Notes inMath. No. 72,The syntax and semantics of infinitary languages, Springer- Verlag, Berlin, Heidelberg, New York, 1968, pp. 36-64.
  • [2] A. Ehrenfeucht and A. Mostowski, Models of axiomatic theories admittingauto- morphisms, Fundamenta Math., 43 (1956), 50-68.
  • [3] P.Erdos and A. Hajnal, Unsolved problems in set theory, Proc. of Symp. in Pure Math. XIII Part I A.M.S. Providence, R.I.,(1971), 17-48.
  • [4] P.Erds, A. Hajnal and R.Rado, Partitionrelations for cardinalnumbers, Acta
  • [5] P. Erdos and M. Makkai, Some remarks on set theory X, Studia Scientiarum Math. Hungarica, 1 (1966), 157-159.
  • [6] H. J. Keisler, Formulas with linearly ordered quantifiers, Lecture Notes in Math. No. 72, The syntax and semantics of infinitary languages, Springer-Verlag,Berlin, Heidelberg, New York, (1968), 96-130.
  • [7] M. Makkai, Structures elementarily equivalent to models of higher power relative to infinitarylanguages, Notices of Amer. Math. Soc, 15 (1969), 322.
  • [8] W. Mitchell, On the cardinality of dense subsets of linear ordering II, Notices of Amer. Math. Soc, 15 (1968), 935.
  • [9] M. Morley, Categoricity in power, Trans. Amer. Math. Soc, 114 (1965), 514-538.
  • [10] M. Morley, Omittingclasses of elements, The theory of models, edited by J. W. Addison, L. Henkin and A. Tarski, Proceedings of the 1964 Intern. Symp. for Logic, Berkeley (Amsterdam, North-Holland Publ. Co.), (1965), 265-274.
  • [11] F. P. Ramsey. On a problem of formallogic, Proceedings of the London Math. Society, Ser. 2, 30 (1929), 328-384.
  • [12] S. Shelah, Stable theories, Israel J. Math., 7 (1969), 187-202.
  • [13] S. Shelah, Finite diagrams stable in power, Annals of Math. Logic, 2 (1790), 69-116.
  • [14] S. Shelah, On the number of non-almost isomorphic models, Pacific J. Math., 36 (1971), 811-818.
  • [15] S. Shelah, Stabilityand the fc.p.)Model theoretic properties of formulas in first- order theories, Annals of Math. Logic, 3 (1971), 271-362.
  • [16] S. Shelah, On the numberof non-isomorphic models of an unstablefirst-order theory, Israel J. Math., 9 (1971), 473-487.
  • [17] P. C. Eklof, On the existence of Loo,-indiscernible, Proc Amer. Math. Soc, 25 (1970), 798-800.
  • [18] P. Erds and A. Hajnal, Unsolved and solved problems in set theory, to appear (in the Proc of Tarski Symp.?)
  • [19] M. Sauer, On the density of families of sets, J. Combinatorial Theory, Series A,