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CM-triviality is the condition that whenever $A (= B$ and $c$ are such that
$\operatorname{acl}^{\operatorname{eq}}(Ac) \cap \operatorname{acl}^{\operatorname{eq}}(B) = \operatorname{acl}^{\operatorname{eq}}(A)$, the type
$\operatorname{tp}(\operatorname{Cb}(c/A)/\operatorname{Cb}(c/B)$) is algebraic.

The authors consider weakening this condition by requiring in the
conclusion only that the type be almost internal to a fixed collection of
types $\Sigma$. They term this ``2-tightness'' with respect to $\Sigma$. They
draw the analogy with corresponding weakenings of 1-basedness, which they term
``1-tightness'', viewing the Canonical Base Property as an example.

The authors proceed to generalise to 2-tight theories the structural results
on CM-trivial theories obtained by Pillay \cite{PillayGeomFork}. There it was
shown that in a CM-trivial theory, there are no interpretable infinite fields
and any interpretable group of finite Morley rank is nilpotent-by-finite. Here
this is generalised to: in a stable theory which is 2-tight with respect to
$\Sigma$, any interpretable field is $\Sigma$-internal and any interpretable
group of finite Lascar rank is nilpotent-by-(almost $\Sigma$-internal).

The proof follows in part the line of Pillay's - involving an analysis of
``bad groups'', which here are shown must be $\Sigma$-internal - but the
result does not follow so directly and further use of stable group theory is
involved.

\begin{thebibliography}{Pil95}

\bibitem[Pil95]{PillayGeomFork}
Anand Pillay.
\newblock The geometry of forking and groups of finite {M}orley rank.
\newblock {\em J. Symbolic Logic}, 60(4):1251--1259, 1995.

\end{thebibliography}

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