MAXIMALITY OF TWO-VALUED LOGICS
Alexej P. Pynko · 2025
As a key observation, we prove that any two-valued matrix with both distinguished and non-distinguished value is embedable into any submatrix of its direct power with both distinguished and non-distinguished values, in which case they define the same two-valued logic, and so this is defined by any model of it with both distinguished and non-distinguished values. As a consequence, we conclude that any fragment of the classical logic is [inferentially] maximal, whenever it has [no] theorems.