Individual axioms are almost always part of a larger axiomatic system. Other approaches provide formal semantics of programming languages including axiomatic semantics and operational semantics. Lattices can also be characterized as algebraic structures satisfying certain axiomatic identities. In philosophy "first principles" are often somewhat synonymous with "a priori", datum and axiomatic reasoning. These texts, written in an austere and axiomatic style, emphasized rigorous presentation and set-theoretic foundations. Thermodynamic equilibrium is an axiomatic concept of thermodynamics. For undecidability in axiomatic mathematics, see List of statements undecidable in ZFC. Category theorists have proposed topos theory as an alternative to traditional axiomatic set theory. In this sense, formalism lends itself well to disciplines based upon axiomatic systems. Another topic that developed from axiomatic studies of projective geometry is finite geometry. That said, ontology is crucial for the axiomatic language frameworks. Placing Euclidean geometry on a solid axiomatic basis was a preoccupation of mathematicians for centuries. The theory is based on an axiomatic approach. It is the logic used in mathematics and other axiomatic systems such as formal logic. In everyday mathematics the best choice may be informal use of axiomatic set theory.