Journal of Symbolic Logic

Discouraging results for ultraimaginary independence theory

Itay Ben-Yaacov

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Abstract

Dividing independence for ultraimaginaries is neither symmetric nor transitive. Moreover, any notion of independence satisfying certain axioms (weaker than those for independence in a simple theory) and defined for all ultraimaginary sorts, is necessarily trivial.

Article information

Source
J. Symbolic Logic, Volume 68, Issue 3 (2003), 846- 850.

Dates
First available in Project Euclid: 17 July 2003

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1058448443

Digital Object Identifier
doi:10.2178/jsl/1058448443

Mathematical Reviews number (MathSciNet)
MR2004f:03063

Zentralblatt MATH identifier
1060.03050

Subjects
Primary: 03C45: Classification theory, stability and related concepts [See also 03C48] 03C95: Abstract model theory

Keywords
dividing independence ultraimaginaries

Citation

Ben-Yaacov, Itay. Discouraging results for ultraimaginary independence theory. J. Symbolic Logic 68 (2003), no. 3, 846-- 850. doi:10.2178/jsl/1058448443. https://projecteuclid.org/euclid.jsl/1058448443


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References

  • Itay Ben-Yaacov, Ivan Tomašić, and Frank O. Wagner Constructing an almost hyperdefinable group, preprint,2001.
  • Bradd Hart, Byunghan Kim, and Anand Pillay Coordinatisation and canonical bases in simple theories, Journal of Symbolic Logic, vol. 65 (2000), pp. 293--309.
  • Byunghan Kim Forking in simple unstable theories, Journal of the London Mathematical Society, vol. 57 (1998), no. 2, pp. 257--267.
  • Frank O. Wagner Simple theories, Kluwer Academic Publishers,2000.