🔢 Math MOC


There are two definitions of a theory:

  • a set of axioms (facts) about specific constants, functions, and predicate symbols
  • the set of all the theorems provable from those axioms. (Sometimes called the closure.)

A theory is built on Logic.

Model of the Theory

An interpretation in which all the axioms of the theory are true is called a model of the theory.

When constructing a theory, we usually have at least one model in mind, which is called the standard or normal interpretation of the theory.

Some reasoning tools can ensure that an argument is considered only in the standard interpretation of the theory.

Theoretical Analysis

I like when you use Theory to do Proofs, there’s a beauty in that.