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Logic lll - Incompleteness and Undecidability (PH9F1-20)

Programme content

Introducing students to results and techniques pertaining to advanced topics in logic pertaining to formal arithmetic, Gödel's Incompleteness Theorems, and computability theory.

By the end of the module the student should be able to....

  • Demonstrate advanced knowledge of Gödel’s First and Second incompleteness Theorem’s and related results and definitions pertaining to formal arithmetic and computability (e.g. primitive recursive functions, arithmetic representability, proof predicates, self-referential statements, decidable and undecidable theories).
  • Define concepts and state results with precision, both within formal and discursive contexts.
  • Obtain a systematic understanding of the significance of technical concepts and results and be able to comprehensively interpret and evaluate their relation to broader topics in philosophy and mathematics (e.g. the difference between soundness and consistency, and truth and provability).
  • Independently construct derivations in formal systems as well as soundly reason about these systems mathematically.

Module Director:

Walter Dean

Sample reading list (PDF Document)

Topics covered

TBD

Timing and CATS

This module is running in the Spring Term and is worth 20 CATS.