Math 571 - Mathematical Logic

• Prerequisites: Math 234 or equivalent.
• Frequency: Fall(I)
• Student Body: majors in mathematics, computer science and philosophy. Graduate students in related areas
• Credits: 3. (X-A)
• Recent Texts: Herbert Enderton: "A Mathematical Introduction to Logic", or Martin Goldstern, Haim Judah: "The Incompleteness Phenomenon : A New Course in Mathematical Logic"
• Course Coordinator: Steffen Lempp
• Background and Goals: This course provides an introduction into mathematical logic, including the syntax and semantics of first-order languages, a formal calculus for proofs, Godel's Completeness Theorem and the compactness theorem, nonstandard models of arithmetic, decidability and undecidability, and Godel's Completeness Theorem. It is particularly suitable for majors in mathematics, computer science and philosophy.
• Alternatives: None.
• Subsequent Courses: Math 770.

Content coverage:

• Propositional logic: Connectives and proposition symbols. Formation rules. Parsing sequences for wffs and induction on wffs. Formal tableau proofs. Models and truth values. Soundness and completeness theorems.
• Predicate logic: Logic with quantifiers, variables, and predicate symbols. Formation rules. Models, valuation of variables, and truth values. Tableau proofs. Soundness and completeness theorems. Direct proofs and informal proofs in the usual mathematical style.
• Full predicate logic: Predicate logic with equality and function symbols. Formation rules and models. Tableau proofs with equality substitutions. Examples from calculus, set theory, and group theory. Peano arithmetic and formal induction. Soundness and completeness.
• Undecidability: Machine computability. Godel numbers and universal machines. Church's Thesis. Examples of undecidable problems including the halting problem. Undecidability of predicate logic and the Godel incompleteness theorem.