This says that there is no valuation which makes all the sentences mentioned on the left side of ⊨ true whilst making 𝒞 false.
To:
This says that there is no valuation which makes all the sentences mentioned on the left side of ⊨ true whilst making all the sentences on the right side false.
This would make it easier to understand how 𝒜 ⊨ is another way of saying that 𝒜 is a contradiction.
In section 12.5, change:
To:
This would make it easier to understand how 𝒜 ⊨ is another way of saying that 𝒜 is a contradiction.
The A in the first AS in 18.5 Proceed indirectly should probably be an 𝒜.
In 23.2 Names it seems unnecessary to include the following sentence:
Most readers will already be familiar with the fact that many full names are reused and won't need a second example of it as proof.