math logic

Project

Design your own small axiom system.

• You should have four axioms and 4 theorems.

• You must submit at least one consistency model for your system, although having more than one would be great. Note: two consistency models are not required for an A.

• For each axiom, either construct an independence model or prove it is dependent upon the other axioms. Having more than one dependent axioms will negatively impact your grade.

• Submit a proof for each of your theorems.

• You must type this project! It should be easily readable, in a font that doesn’t cause eyestrain. It should be obvious where your proofs begin and end.

• Your consistency model and independence models should be done on a computer. Hand drawing your models will negatively impact your grade.

• You must submit a separate cover sheet containing your name, axioms and theorems for quick reference.

• Your project must be stapled or with a binder clip (paper clip will not suffice). Do not staple the cover sheet to the project.

• Creativity will be appreciated. But you will not lose points if you use point and line.

Deadlines

Each deadline is at the start of class.

Due Thursday November 2: A consistency model(s) and a list of at least 10 possible Axioms/Theorems based on your model. The Axioms must be typed. Worth 5 points.

Due Tuesday November 14: One theorem, it’s proof, and one independence model you want written feedback on. The Axioms, theorem, and proofs must be typed. Worth 5 points.

Due Tuesday November 28: Optional One theorem and it’s proof. This can be the same or a different one from the previous check point. It must be typed.

Due Thursday December 7: Final project. Hard copy and electronic copy uploaded to Moodle by the start of class. Worth 90 points.