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Adding linear orders

  • Saharon Shelah (a1) and Pierre Simon (a2)
Abstract
Abstract

We address the following question: Can we expand an NIP theory by adding a linear order such that the expansion is still NIP? Easily, if acl(A)=A for all A, then this is true. Otherwise, we give counterexamples. More precisely, there is a totally categorical theory for which every expansion by a linear order has IP. There is also an ω-stable NDOP theory for which every expansion by a linear order interprets pseudofinite arithmetic.

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[1] John Baldwin and Michael Benedikt , Stability theory, permutations of indiscernibles, and embedded finite models, Transactions of the American Mathematical Society, vol. 352 (2000), no. 11. pp. 49374969.

[3] R. Graham , B. Rothschild , and J.H. Spencer , Ramsey theory, 2nd ed., New York: John Wiley and Sons. 1990.

[4] Wassily Hoeffding , Probability inequalities for sums of bounded random variables, Journal of the American Statistical Association, vol. 58 (1963), no. 301, pp. 1330.

[6] Akito Tsuboi . Random amalgamation of simple theories, Mathematical Logic Quarterly, vol. 47 (2001), no. 1, pp. 4550.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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