Theories

List of theories:

Definition

A theory is a set of axioms (facts) about specific constants, functions, and predicate symbols.

It is also sometimes defined as the set of all theorems provable from these axioms (called a closure).

Info

Theories come in two flavours:

General, mathematical theories
- Well-known theories developed by others, such as theories for arithmetic, sets, sequences
Particular theories
- We make them ourselves

Axioms must be consistent, otherwise we can prove anything.

Standard (Normal) Interpretation

Definition

The standard or normal interpretation of a theory is the intended interpretation of a theory where the axioms of that theory are all true