  The parenthesis-free symbolism was closely associated with some ideas of Polish logicians concerning the good properties of formal systems. Of course, any correct logical system should be consistent and, if possible, syntactically and semantically complete. It should also be based on independent sets of primitive terms and axioms. The Warsaw School of Logic strongly emphasized the last property, often considered secondary. Thus, the dependence of primitive terms or axioms was regarded as an essential defect. Moreover, some additional structural properties of logical systems were recommended: (a) a system with fewer primitive concepts is better; (b) a system with fewer axioms is better; (c) if we define the length of an axiom system as the number of symbols occurring in all of its axioms, the shortest axiom system is the best; (d) a system with fewer different symbols is better; (e) if we define an organic theorem as one which has no other theorem inside it (for example, the formula CpCqq is not an organic theorem), organic axioms are better than non-organic ones. Thus, the ideal axiom system consists of a sole organic axiom of the shortest possible length, provided that it is consistent. Requirements (a)-(f) apply particularly well to propositional calculus. They became the guiding principles of many logical investigations in the Warsaw School of Logic. Logicians of this school also made precise many important metalogical concepts, including those of the logical matrix, consequence operation, deductive system and model.