A sequence of formulas is said to be **-inconsistent** if for every of size , is inconsistent. That is, a sequence of formulas is -inconsistent if any of the formulas in the sequence is jointly inconsistent. For example, 2-inconsistency is equivalent to pairwise inconsistency.

Typically, -inconsistency is only considered when the are all the same formula.

This notion is rigged to behave very well with respect to indiscernible sequences. Specifically:

- If is an indiscernible sequence, then is inconsistent if and only if it is -inconsistent for some .
- If is arbitrary, and is -inconsistent, then this is witnessed in the EM-type of . Consequently, if is an indiscernible sequence extracted from , then will also be -inconsistent, for the same .

-inconsistency plays a basic role in the definitions of dividing, forking, and their variants (such as thorn-forking). ::: ::: :::