
Foundations:Mathematical Logic And Set Theory
… when we are set to work and we take ???? to be our foundational theory, then we fix one universe of set theory that we work in. … When you are done working with this universe you throw it in the bin, and get another when you need to. Or you can save that universe in a scrapbook if you like.  Asaf Karagila
 SET THEORY: CARDINAL AND ORDINAL NUMBERS Klaus Kiaser University of Houston s
 Cardinal and Ordinal Numbers Klaus Kaiser University of Houston April 9, 2007
 Set Theory:The Natural Numbers Peter J. Kahn Cornell University Spring 2009
 A Problem Course in Mathematical Logic Version 1.6 Stefan Bilaniuk Trent University 2011
 Mathematical Logic Vladimir Lifschitz University of Texas January 16, 2009
 Mathematical Logic Lou van den Dries University of Wisconsin Urbana Champaign Fall Semester 2007
 Mathematical Logic I Kevin C Clement University of Massachucetts Fall 2011
 Mathematical Logic II Kevin C Clement University of Massachucetts Fall 2011
 Mathematical Logic II Kevin C. Clement University of Massachuecetts Almherst 2012
 Mathematical Logic I Simon Thomas Rutgers University Spring 2013
 An Introduction To Mathematical Logic Michal Walicki University of Bergen
 Algebraic Methods F. Oggier Nanyang Technological University November 11, 2011
 Mathematical Logic Arnold W. Miller University of Wisconsin Fall 1995
 Mathematical Logic Stephen G. SimpsonThe Pennsylvania State University February 7, 2011
 Mathematical Logic Helmut Schwichtenberg Mathematisches Institut der Universität München
 Logic Jonathan Pila Mathematical Institute University of Oxford
 Logic and Computation Lecture notes Jeremy Avigad Carnegie Mellon University The syntax and semantics of firstorder logic, completeness,compactness, and other topics.
 Ordered Sets Tero Harju University of Turku Finland 2006 (2012)
 Set Theory: Notes on Forcing Judith Roitman Kansas University May 13, 2010
 SET THEORY William A. R. Weiss University of Toronto October 2, 2008
 Model Theory and its Applications Pete L.Clark University of Georgia
 2010 SUMMER COURSE ON MODEL THEORY PETE L. CLARK University of Georgia
 Logic For Computer Science :Foundations of Automatic Theorem Proving Jean Gallier University of Pennsylvania June 2003
 Ordered Sets Mariusz Wodzicki University of California at Berkeley March 13 , 2013
 Elementary Set Theory With a Universal Set 2nd edition by Randall Holmes
 Model Theory Cameron Freer MIT Spring 2009
 Axiomatic Set Theory Boris Zilber Oxford University January 14, 2013
 Set Theory Jonathan Pila Oxford University Spring 2013
 Model Theory and Set Theory Rahim Moosa University of Waterloo Fall 2012
 Sets and Cardinality C. F. Miller University of Melbourne Semester 1, 2000
 Axiomatic Set Theory I by A. C. WalczakTypke University of Helsinki April 27, 2009
 Fundamentals Of Model Theory William Wiess and Cherie D' Mello University of
Toronto Complexity Theory I Oded Goldreich Weizmann Institute of Science, Israel
 Foundations of Mathematics Stephen G. Simpson The Pennsylvania State University October 1, 2009
 Foundations of Mathematics I Set Theory Ali Nesin Istanbul Bilgi University Kustepe Sisli Istanbul Turkey
 Predicate Logic Jeff Paris University of Manchester 2013
 Model Theory Anand Pillay University of Waterloo December 9, 2002
 Computability Theory and Applications: The Art of Classical Computability Robert Irving Soare The University of Chicago VOLUME I draft December 22, 2011
 Logic and Verification Clark W. Barrett NYU
 Logic In Computer Science Fall 2009 Clark Barrett NYU
 Set Theory Sam Buss USCD Fall 2012 – Winter 2013
 Introduction to Symbolic Logic Gary Hardatree University of Massachucetts Amherst Fall 2013
 Introduction to Logic Kevin C. Klement University of Massachucetts Amherst Spring 2013
 Computation Theory and Formal Languages Jean Gallier and Andy Hicks University of Pennsylvania Jean Gallier is a completely fascinating and awestriking person in current academia I'd love to meet someday. He was born of French parentage got his BA in France at the age of 17, a civil engineering degree 6 years later and then completing his Ph.D in applied mathematics/computer science at UCLA 6 years after that.Currently a professor in both the Computer Science and Mathematics departments of the University of Pennsylvania, he's known mostly for his work in theoretical computer science and several important breakthroughs in the burgeoning science of computer graphics. Many of these breakthroughs have come as a result of Gallier's deep understanding of basic mathematics and its applications,such as algebra and graph theory. Recently, in order to strengthen his background in theoretical mathematicswhich he has found so useful in both his basic research and that of his studentshe spent several years faithfully attending many of the graduate courses in mathematics at the University of Pennsylvania,taking very detailed notes and doing all the exercises in each class. The result has been an extraordinary set of lecture notes and book drafts on advanced mathematics for computer scientists and other applied mathematicansnotes that are incredibly detailed and wonderfully intuitive without sacrificing rigor. Several of these lecture series have been published as expensive SpringerVerlag textbooks,much to the chagrin of most of us who first discovered them at his site for free. Gallier's identified several of the longer lecture notes as "book drafts"which means I strongly advise students to download as many as you can before he sends them off for publication. Dr.Gallier has made it very clear at his site that while actually posting these documents anywhere else on the web constitutes copyright infringement, downloading them for personal use and posting links to them at his webpage are fine. That's what I'm doing,hopefully increasing the knowledge of these terrific presentationsand eventually making Dr. Gallier a fortune in the process when they're published. (You owe me a favor,pal........LOL) First up are the lectures from Gallier's course on computation and programming language theory. Like most such courses, he develops the discrete mathematicssuch as basic logic and set theoryneeded to understand the foundations of formal language construction and syntax. Unlike most such courses, he develops far more mathematics then usualsuch as automata theory and directed graphs and includes many real world examples where this theory is used, such as DNA computing. These terrific notes will be a treasure for both serious computer science students and mathematics students (who really should,myself included,be much more familiar with the actual theory of computation then most of us actually are.)
 FIRST ORDER LOGIC AND GODEL INCOMPLETENESS ANUSH TSERUNYAN UCLA 2009
 Topics in Logic and Foundations Stephen G. Simpson Pennsylvania State University
 Computability, Unsolvability, Randomness Stephen G. Simpson Pennsylvania State University February 5, 2009
 Degrees of Unsolvability Stephen G. Simpson Pennsylvania State University
 Propositional Logic Mike Prest University of Manchester April 16, 2013
 Model Theory and Modules Mike Prest University of Manchester May 22, 2006
 Descriptive Set Theory David Marker University of Illinois Chicago
 Model Theory Boris Zibler Mathematical Institute University of Oxford 2013
 Set theory Peter J. Kahn Cornell University Spring 2009
 SET THEORY Wiliam Weiss University of Toronto
 SET THEORY Rienhard Shiultz University of Illinois Chicago/UNIVERSITY OF CALIFORNIA RIVERSIDE FALL 2012
 Set Theory Ted Slider Cornell University 2010
 Set Theory Gregory Wheeler Carnegie Mellon University
 Modern Set Theory 2nd Edition Judith Roitman University of Kansas December 6, 2011
 AN ELEMENTARY THEORY OF THE CATEGORY OF SETS (LONG VERSION) WITH COMMENTARY F. WILLIAM LAWVERE
 BOOLEAN FUNCTIONS TOM SANDERS University of Cambridge
 A Modern Formal Logic Primer 2 volumes by Paul Teller UC Davis
 Fundamentals of Model Theory William Weiss and Cherie D’Mello Department of
Mathematics University of Toronto Computability and Incompleteness Jeremy Avigad Carnigie Mellon University Version: January 9, 2007
 Gödel's Incompleteness Theorems Mathematical Institute  University of Oxford
 Good old fashioned model theory Harold Simmons University of Manchester
 Logic and Proof Lawrence C Paulson Computer Laboratory University of Cambridge
 Proof, Sets, and Logic M. Randall Holmes Boise State University November 30, 2012
 Recursion Theory Lou van den Dries University of Wisconsin UrbanaChamplaign Fall 2011
 Incompleteness via the halting problem Jeremy Avigad Carnagie Mellon University
February 21, 2005 Classical and constructive logic Jeremy Avigad Carnegie Mellon University
September 19, 2000 Set Theory Gary Hardegree University of Massachucetts
 Proof Theory:An Introduction Samuel R. Buss University of California San Diego
 Michal Walicki's Introduction to logic 2011 draft version
 Unraveling the Mysteries of Infinity Jimmie Lawson Louisiana State University
2008 Introduction to Mathematical Logic J. Adler, J. Schmid May 2, 2007
 Model Theory, Universal Algebra and Order J. Adler, J. Schmid, M. Sprenger
January 18, 2006 First order logic and Computability B. Csima transcribed by: J. Lazovskis University of Waterloo April 9, 2012
 AN INVITATION TO MATHEMATICAL LOGIC Thomas Wieting Reed College,
2012 Foundations of Mathematics David Mond University of Warwick 2012
 Proof Theory: From the Foundations of Mathematics to Applications in Core Mathematics UlrichKohlenbach
 Introduction To Proof Theory Gilles Dowek Ecole Polytechnique
 proof theory & philosophy Greg Restall University of Melbourne
 Model theory and constructive mathematics Thierry Coquand
 Complexity Theory Oded Goldreich Weizmann Institute of Science Israel July 31, 1999
 Mathematical Logic Thomas Simon Rutgers University
 Introduction to Set Theory Kenneth Harris University of Michigan
 Notes on Mathematical Logic David W. Kueker University of Maryland
 Foundations of Mathematics Richard Williamson Norwiegian University of Science and Technology Fall 2013
 Axiomatic Set Theory Christopher Cooper McQuarrie University
 Model Theory lecture notes written by Ambrus Pal Imperial College from
the lectures of Hans Liebeck at Imperial College 2008 Logic Course Material for B1a Jochen Koenigsmann Mathematical Institute University of OxfordGodel’s Incompleteness Theorems Hilary Term 2012 Daniel Isaacson Oxford University
2013AN INTRODUCTION TO SET THEORY William A. R. Weiss October 2, 2008