  Nguyen (2016, 2017) claimed that he has developed a simplifying set of the
Kohlberg criteria that involves checking the balancedness of at most $(n-1)$
sets of coalitions. This claim is not true. Analogous to Nguyen and Thomas
(2016), he has incorrectly applied the indirect proof by $(\phi \Rightarrow
\bot) \Leftrightarrow \neg \phi$. He established in his purported proofs of the
main results that a truth implies a falsehood. This is a wrong statement and
such a hypotheses must be rejected (cf. Meinhardt (2015,2016a,2016b,2017)).
Executing a logical correct interpretation ought immediately lead him to the
conclusion that his proposed algorithms are deficient. In particular, he had to
detect that the imposed balancedness requirement on the test condition
$(\cup_{j=1}^{k}\,T_{j})$ within his proposed methods cannot be appropriate.
Hence, one cannot expect that one of these algorithms makes a correct
selection. The supposed algorithms are wrongly designed and cannot be set in
any relation with Kohlberg. Therefore, our objections from (Meinhardt,2017) are
still valid with some modifications. In particular, he failed to work out
modified necessary and sufficient conditions of the nucleolus.
