Advanced Topics in Philosophical Logic (351-0-21)
Topic
Set Theory and the Infinite
Instructors
Sean Christopher Ebels Duggan
847/491-2553
Kresge 3-443
Meeting Info
Lunt Hall 101: 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.
Contact Prof. S. Ebels Duggan for permission number.
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: Reserved for Graduate Students.
Prerequisite: Students must have completed either PHIL 250 or MATH 300 in order to enroll in this course.
Add Consent: Department Consent Required