Ma6/106c Spring 2026: Logic
Caltech, Linde Hall Room 187, Tuesday-Thursday 1:00-2:30 pm; the TA for the class is Edward Hou
Instructor:
Matilde Marcolli
This class provides a general introduction to mathematical logic. The content of the class is being revised (compared to previous years) so it is currently in an "experimental phase": the usual material previously covered in Ma6c will be included (propositional and first order logic and computability) and additional complementary topics will be added at the discretion of the instructor. The class is offered Letter Grade with the option of Pass/Fail. The students workload will consist of completeing an assigned number of homework problems and preparing a final presentation on a topic of choice selected from the reading material posted on this page. Homework policy: collaboration (exclusively with human collaborators who are registered students in this same class) is allowed and strongly encouraged, but solutions should then be written up individually.
Slides of Lectures
Slides of lectures will be posted here as the class progresses
Summary of lectures
- Tuesday March 31:
- Thursday April 2:
- Tuesday April 7:
- Thursday April 9:
- Tuesday April 14:
- Thursday April 16:
- Tuesday April 21:
- Thursday April 23:
- Tuesday April 28:
- Thursday April 30:
- Tuesday May 5:
- Thursday May 7:
- Tuesday May 12:
- Thursday May 14:
- Tuesday May 19: cancelled due to travel
- Thursday May 21:
- Tuesday May 26:
- Thursday May 28:
- Tuesday June 2: students presentations (room and schedule to be announced)
- Thursday June 4: students presentations (room and schedule to be announced)
Reading Materials
There is no specific textbook for the class. Some suggested
reading material will be posted here.
Books
- pdf Yuri I.Manin, "Logic for Mathematicians"
- pdf I.Moerdijk, J.van Oosten, "Sets, Models and Proofs"
Papers (more material will be added here as the class progresses):
- pdf F.W.Lawvere, "An elementary theory of the category of sets"
- pdf F.W.Lawvere, "Diagonal Arguments and Cartesian Closed Categories"
- pdf S.A.Kurtz, "A Brief Introduction to the Intuitionistic Propositional Calculus"
- pdf D.Trufas, "Intuitionistic Propositional Logic in Lean"
- pdf
S. Adam-Day, N. Bezhanishvili, D. Gabelaia V. Marra, "The Intermediate Logic of Convex Polyhedra"
- pdf B.M.Bumpus, Z.A.Kocsis, "Degree of satisfieability in Heyting Algebras"
- pdf C.Lutz "Modal Logics for Computer Science"
- pdf
M.E.Coniglio, L.Prieto-Sanabria, "Modal logic S4 as a paraconsistent logic with a topological semantics"
- pdf
I. Garcia-Contreras, V.K.H. Govind, S Shoham, A Gurfinkel "Fast Approximations of Quantifier Elimination"
- pdf Ta Le Loi, "An Introduction to Semialgebraic Sets"
- pdf A Ghorbani, "The tame geometry of o-minimal structures"
- pdf C.Miller "Notes on tameness in model-theoretic structures"
- pdf N.S.Yanofsky, "A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points"