MATH 712 -- MATHEMATICAL LOGIC I:
		FORMAL LANGUAGES AND THEIR MODELS
			
TIME & ROOM: MWF at 1:00 in MTH 0304

INSTRUCTOR:  David W. Kueker
	     Office:  MATH 1102
	     Phone:   405-5052
	     e-mail:  dwk@math.umd.edu
	     Office hours: by appointment

DESCRIPTION: MATH 712-713 is a self-contained introduction at the graduate
	level to the main areas of modern mathematical logic, exclusive of
	set theory.  No previous study of logic is assumed.  Math 712 begins
	with an introduction to first-order languages and a proof of Godel's
	Completeness Theorem.  It continues with an introduction to the
	research area of model theory.  Examples and applications in algebra
	and graph theory will be included.  Math 713 treats the topics of
	incompleteness, undecidability and computability.  It begins with
	the Incompleteness Theorems of Godel and continues with other
	undecidability results, including Hilbert's 10th Problem.  The text
	consists of notes which will be provided by the instructor.

OUTLINE:			MATH 712

	A.  Elementary Logic
	    1.  First-order languages
	    2.  Formal deductions
	    3.  Theories and their models
	    4.  Completeness, compactness, Lowenheim-Skolem theorems
	B.  Model Theory
	    1.  Realizing and omitting types
	    2.  Elementary extensions and chains
	    3.  Prime and saturated models
	    4.  Model construction techniques

				MATH 713

	C.  Incompleteness and Undecidability
	    1.  Effective procedures and computability
	    2.  Recursive functions
	    3.  Godel's incompleteness theorems
	    4.  Undecidable problems
	D.  Recursion Theory
	    1.  Partial recursive functions
	    2.  Turing reducibility
	    3.  Degrees of unsolvability
	    4.  Arithmetic hierarchy

SCHEDULE:	MATH 712 -- Fall 2006
	Chapter 1 -- Sentential Logic -- 4 days
	Appendix 1 - Cardinals -- 1 day
	Chapter 2 -- First Order Logic -- 10 days
	Chapter 3 (part 1) -- The Completeness Theorem -- 4 days
	Midterm Exam --  Monday 23 October
	Chapter 3 (part 2) -- Applications of Completeness - 4 days
	Chapter 4 -- Methods in Model Theory -- 7 days
	Chapter 5 -- Countable Models -- 7 days
	Final Exam -- Friday 15 December 1:30-3:30