In this module, we will explore the power and limits of logical tools and techniques.
The main goals of the module will be to come to grips with some standard ‘metatheoretical’ results about logic: (1) the Soundness and Completeness Theorems, which together show that proofs and models can be used analyse the same consequence relation in two very different ways. (2) The Compactness Theorem and the Löwenheim- Skolem Theorems, which explore some of the limits of first-order classical predicate logic for classifying infinite structures. And most importantly (3) we will work through Gödel’s celebrated Incompleteness Theorems and come to grips with what they mean.
The main goals of the module will be to come to grips with some standard ‘metatheoretical’ results about logic: (1) the Soundness and Completeness Theorems, which together show that proofs and models can be used analyse the same consequence relation in two very different ways. (2) The Compactness Theorem and the Löwenheim- Skolem Theorems, which explore some of the limits of first-order classical predicate logic for classifying infinite structures. And most importantly (3) we will work through Gödel’s celebrated Incompleteness Theorems and come to grips with what they mean.
Course Type: 2023-2024 Modules
Shared Course: No
Feeder Course: No