Advanced Topics in Philosophical Logic (351-0-20)

Topic

Set Theory and the Infinite

Instructors

Sean Christopher Ebels Duggan
847/491-2553
Kresge 3-443

Meeting Info

Parkes Hall 214: Mon, Wed, Fri 10:00AM - 10:50AM

Overview of class

Axiomatic set theory was developed to provide a background theory for mathematics more generally, as well as to address paradoxes arising from a naive conception of sets. It also generates a powerful theory of the infinite that, interestingly, leaves open some of the most natural questions it raises--chief among them Cantor's Continuum Hypothesis on the relative size of the collection of real numbers. This class will elaborate the iterative conception of sets, its relationship to the standard ZFC axioms, and will develop the theory of infinite ordinals and cardinals with the goal of establishing classical independence results.

Learning Objectives

Practice writing of proofs that reference axioms. Appreciate the philosophical questions surrounding axioms and independence in set theory. Attain skill and facility in proving results in and about ZFC.

Class Materials (Required)

All class materials will be available at the library at NO cost to students.

Nik Weaver, Forcing for Mathematicians

Class Materials (Suggested)

We will also use various freely available online books.

Class Notes

Final Exam - In Class

Enrollment Requirements

Enrollment Requirements: Prerequisite: Students must have completed either PHIL 250 or MATH 300 in order to enroll in this course. Prerequisite: Students must have completed either PHIL 250 or MATH 300 in order to enroll in this course.
Add Consent: Instructor Consent Required