Consistency and Completeness

# Consistency and Completeness - Consistency Independence and...

This preview shows pages 1–3. Sign up to view the full content.

Consistency, Independence, and Completeness of a Set of Axioms Recall that an axiomatic system has four components 1. A set of undefined terms 2. A set of defined terms 3. A set of AXIOMS (or Postulates) 4. A set of THEOREMS together with their proofs EXAMPLE of an Axiomatic System: Four-Point Geometry Undefined Terms: Point, line, on Axioms: Ax 1: There exist exactly four points. Ax 2: (Any) Two distinct points are on exactly one line. Ax 3: Each line is on exactly two points. Definition: A MODEL for an axiomatic system is a structure (in a “real world” context or in an abstract context) and an interpretation (from within that structure) of the undefined terms such that all the Axioms become TRUE statements about the structure.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Definition: A set of Axioms is Inconsistent if it is possible to prove one statement and its negation as both being TRUE. A set of Axioms is Consistent if it is Not Inconsistent. The set of axioms in an axiomatic system is proven to be
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

Consistency and Completeness - Consistency Independence and...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online