When emailing me, please use plain text (7 bit ASCII) only. That is, only the characters found on a standard English language keyboard; no curved quotation marks, curved apostrophes, accented letters, Greek letters, etc. In particular:
In the first few weeks, we intend to present mostly complete proofs of several versions Gödel's Incompleteness Theorem, with some discussion of refinements. The rest of the course will be devoted to forcing and some applications, particularly independence of the Continuum Hypothesis from Zermelo-Frankel set theory with the Axiom of Choice.
Formal logic is not a prerequisite, but will also not be presented in detail. Instead, an overview will be given of how it works, which, I hope, will be sufficient for understanding the ideas of the Incompleteness Theorem and forcing.
For forcing, I will follow parts of Nik Weaver, Forcing for Mathematicians, World Scientific, 2014. Again, it will be mostly earlier chapters. The library does not have a paper copy of this book, although you can try interlibrary loan. It has the same three ebook options as for Smullyan's book.
I am also using two other books as references: Herbet Enderton, A Mathematical Introduction to Logic, second edition, Academic Press, 2001, and Kenneth Kunen, Set Theory: An Introduction to Independence Proofs, North-Holland, 1980. There is a "total rewrite" of the second of these, Set Theory, College Publications, 2011. One big change is that the newer version uses model theory as one of the basic techniques, while, in the older version, "pains were taken to avoid model-theoretic methods". Enderton's book is an upper division undergraduate textbook. Its Chapter 1 is about sentiential logic (no quantifiers). Its Chapter 3 has proofs of Gödel's First and Second Incompleteness Theorems, and its Chapter 4 has a small amount of information on second order logic. Throughout the book, there are discussions of computability.
This page maintained by N. Christopher Phillips, email. Please email plain text (7 bit ASCII) only (no web page coded files, Microsoft Word documents, binary characters, etc.; see above for more).
Last significant change: 17 September 2018.