P350 | 3597 | McCarty

Note: This class meets with P551, Philosophy and the Foundations of Math The first goal of this joint advanced undergraduate/graduate course is to acquaint students with the basic foundational ideas and results of axiomatic set theory including those concerning set operations, natural numbers, ordinal numbers, cardinal numbers, transfinite induction and the Axiom of Choice. During the second half of the semester, we will turn to a close study of models of set theory, particularly Boolean-valued models, taking as our goal an understanding of the important independence results, e.g., the independence of the Axiom of Choice. Textbooks: Enderton, Herbert, "Elements of Set Theory," Academic Press. Bell, J.L. "Boolean-Valued Models and Independence Proofs in Set Theory," Oxford University Press. Grading and Assignments: In addition to readings from the textbooks and weekly, written assignments consisting of short essays and exercises in set theory, there will be one written, in-class, midterm examination and a written final examination. Frequent in-class quizzes will also be administered. To an extent, there will be separate requirements and grading scales for undergraduates and graduate students. Note: Graduate students taking this course will be expected to have complete P506. Undergraduates should have completed P251.