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Date: August 23, 2013

This semester I am teaching MATH 557.  MATH 557 is an introductory
course in mathematical logic.  It is suitable for all mathematics

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