Date: August 23, 2013 Subject: advertisement for MATH 557 Dear Mathematics Graduate Students, This semester I am teaching MATH 557. MATH 557 is an introductory course in mathematical logic. It is suitable for all mathematics graduate students. Mathematical logic is an important branch of modern mathematics which grew out of profound investigations of Hilbert, Gödel, Turing, and others into the nature of mathematical reasoning. An important goal of mathematical logic is to develop precise, mathematically rigorous answers to some of the most basic questions in the foundations of mathematics. Some of the questions to be discussed and answered in this course are: What precisely is a mathematical theorem? What precisely is a mathematical definition? What precisely is a mathematical proof? What precisely is a computable function? Topics to be presented in the course include: - propositional calculus - predicate calculus - logical validity and consistency - the tableau method - the completeness theorem (Gödel) - the compactness theorem - explicit and implicit definability - predicate calculus with identity - many-sorted predicate calculus - proof systems - Beth's theorem on implicit definability - theories and models - mathematical theories (e.g., group theory) - foundational theories (e.g., axiomatic set theory) - undecidability of logical validity - incompleteness and undecidability - Gödel's Second Incompleteness Theorem The course is meeting Tuesday-Thursday 9:45-11:00 in 315 McAllister. Chapters 1-5 of my lecture notes http://www.personal.psu.edu/t20/notes/logic.pdf will serve as the textbook for much of the course. The course web page is http://www.personal.psu.edu/t20/courses/math557/. In case you decide to enroll, the Schedule Number is 178483. Best wishes, -- S. Simpson Stephen G. Simpson Department of Mathematics McAllister Building, Pollock Road Pennsylvania State University State College, PA 16802, USA web: www.personal.psu.edu/t20/ email: t20@psu.edu office: 814-863-0775 staff: 814-865-7527 home: 814-238-2274 fax: 814-865-3735