Skip to main content
SpringerLink
Log in

A remark on strict independence relations

  • Published:
Archive for Mathematical Logic Aims and scope Submit manuscript

Abstract

We prove that if T is a complete theory with weak elimination of imaginaries, then there is an explicit bijection between strict independence relations for T and strict independence relations for \({T^{\rm eq}}\). We use this observation to show that if T is the theory of the Fraïssé limit of finite metric spaces with integer distances, then \({T^{\rm eq}}\) has more than one strict independence relation. This answers a question of Adler (J Math Log 9(1):1–20, 2009, Question 1.7).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Adler H.: A geometric introduction to forking and thorn-forking. J. Math. Log. 9(1), 1–20 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  2. Casanovas, E.: Simple Theories and Hyperimaginaries. Lecture Notes in Logic, vol. 39. Association for Symbolic Logic, Chicago, IL (2011)

  3. Casanovas E., Wagner F.O.: The free roots of the complete graph. Proc. Am. Math. Soc. 132(5), 1543–1548 (2004) (electronic)

    Article  MathSciNet  MATH  Google Scholar 

  4. Conant, G.: Neostability in countable homogeneous metric spaces, submitted, arXiv:1504.02427 [math.LO] (2015)

  5. Ealy C., Goldbring I.: Thorn-forking in continuous logic. J. Symb. Log. 77(1), 63–93 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ealy C., Onshuus A.: Characterizing rosy theories. J. Symb. Log. 72(3), 919–940 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  7. Harnik V., Harrington L.: Fundamentals of forking. Ann. Pure Appl. Log. 26(3), 245–286 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kim, B., Pillay, A.: Simple theories. Ann. Pure Appl. Log. 88(2–3), 149–164, (1997) Joint AILA-KGS Model Theory Meeting (Florence, 1995)

  9. Sauer, N.W.: Oscillation of Urysohn Type Spaces, Asymptotic Geometric Analysis, Fields Inst. Commun., vol. 68, Springer, New York, pp. 247–270 (2013)

  10. Shelah S.: Toward classifying unstable theories. Ann. Pure Appl. Log. 80(3), 229–255 (1996)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Notre Dame, Notre Dame, IN, USA

    Gabriel Conant

Authors
  1. Gabriel Conant
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gabriel Conant.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Conant, G. A remark on strict independence relations. Arch. Math. Logic 55, 535–544 (2016). https://doi.org/10.1007/s00153-016-0479-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00153-016-0479-6

Keywords

Mathematics Subject Classification

Search

Navigation