Summary
We define a generalized notion of rank for stable theories without dense forking chains, and use it to derive that every type is domination-equivalent to a finite product of regular types. We apply this to show that in a small theory admitting finite coding, no realisation of a nonforking extension of some strong type can be algebraic over some realisation of a forking extension.
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Research supported by the Deutsche Forschungsgemeinschaft
Thanks as always to Alistair. Research supported by NSERC and FCAR
Partially supported by NSF grant DMS90 06628
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Herwig, B., Loveys, J.G., Pillay, A. et al. Stable theories without dense forking chains. Arch Math Logic 31, 297–303 (1992). https://doi.org/10.1007/BF01627503
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DOI: https://doi.org/10.1007/BF01627503