I am trying to study Mathematical Logic by Chiswell and Hodges.
They prove that for every syntactically consistent set Γ of formulas, there is a Hintikka set Δ s.t. Γ ⊆ Δ.
They describe an algorithm to construct the Hintikka set. The algorithm needs to check whether the addition of the new formula preserves the syntactical consistency of the set. But how is the algorithm able to tell whether that's the case?