Meets:    TR 8:10–9:25am, CR 109.

Instructor:    Eric Moorhouse,   Ross 216,   766-4394.

Prerequisite:     Math 3000 or permission of instructor.

	Textbook (required): Sets, Logic and Categories, Peter J. Cameron, Springer, 1998.		Additional source (optional): Gödel, Escher, Bach: An Eternal Golden Braid, D. Hofstadter, 20th Anniversary Edition, Basic Books, 1999.
	Additional source (optional): Gödel's Theorem: An Incomplete Guide to its Use and Abuse, Torkel Franzén, A. K. Peters, 2005.		Additional source (optional): A Course in Mathematical Logic for Mathematicians, 2nd ed., Yu. I. Manin with B. Zilber, Springer, 2010.
	Further reading (optional): Model Theory: An Introduction, David Marker, Springer, 2002.		Additional Source (optional): Logicomix: An Epic Search for Truth, A. Doxiadis and C. H. Papadimitriou, Bloomsbury, 2009.

  Course announcement

Links/Handouts

•   Syllabus / Policies
•   The n-Category Café. In particular look at the recently posted An Informal Introduction to Topos Theory and any recent posts on mathematics, logic and category theory.
•   Peter Cameron's blog. In particular look at his posts on Mathematics and Logic 1 and 2.
•   On the UW campus, we have access to Manin's book (listed on the syllabus) via SpringerLink. Thanks to Colin for bringing this to my attention.
•   History of the Bernstein-Cantor-Schröder Theorem. Thanks to John Hitchcock for this reference
•   The hat problem and its solution using the Axiom of Choice.
•   Watch the 89-minute BBC documentary Dangerous Knowledge on the fine line between genius and insanity as seen in the life and work of Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing. Gregory Chaitin is one of the narrators.
•   Chow's paper A Beginner's Guide to Forcing describes Cohen's monumental achievement in showing that AC and CH are independent of ZF.
•   Transfinite Induction with an example. (This is the corrected version, now in compliance with Cameron's notation...)
•   Check your email for a link to the Doodle site for scheduling individual appointments for the Oral Examination I.
•   Solutions to Exercise 3.3 in Cameron's book. The proof of the Soundness and Completeness Theorem 3.4 uses results from this exercise.
•   Handout on Applications of Logic to Field Theory distributed March 29
•   Check your email for a link to the Doodle site for scheduling individual appointments for the Oral Examination II.
•   Notes on the Non-Standard Reals. This includes a description of filters and ultrafilters. Handed out on April 19, 2011
•   A followup to the previous handout, here we discuss ultraproduct constructions more generally, giving some more examples and a proof of the Compactness Theorem for first-order logic, using ultraproducts.

/ revised April, 2011