Here is a counterexample to Dan Christensens claim:

1) Every sentence is either (1) a true sentence, (2) a false
sentence, or (3) one of indeterminate truth value.

2) The Liar Sentence (L) is of indeterminate truth value. https://dcproof.com/LiarParadoxV2.htm

The counter example does neither violate Trichotomy, nor
the conclusion that Dan Christensen proved. The Trichotomy
and the conclusion are respected.

Its more based on the fact that the conlusion ALL(b):
... [b e t <=> b e f] ..., which does not imply or require
... [L e t <=> L e f] ..., since this was nowhere stated.

So how is the counter model constructed? Very easily, take
as the set s, the set of propositional formulas, encoded as strings,
i.e. "p", "~p", "q", "p /\ q", etc...

Now define:

t = { "a" e s | a <=> pv~p}
f = { "a" e s | a <=> p&~p}
u = s \ t \ f

Then take L = "p<->~p". We find:

~L e u

Because L e f.

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