Logic and Foundations



Syllabus.
Record of assignments.
Some tips on dealing with proofs.
Some set theory.
Real numbers and Dedekind cuts.
Examples of classical theorems that the intuitionists do not accept..
A sample deduction in L.
Deduction in L of (A --> A).
An example of the Deduction Theorem at work.
Proposition 2.11(b)
Three more useful formulas that are deducible in L.
An Intuitionistic proof that the Propositional Calculus is complete.
Lincoln comes to class.
Some practice with quantifiers.
Some rules of inference in informal predicate logic.
The Agreement and Substitution Theorems.
An example of "v(u')=v'(u)".
The Predicate-Calculus shell of a Propositional-Calculus wf.
Example: The Deduction Theorem in the Predicate Calculus needs restricting.
The Adequacy Theorem for the Predicate Calculus.
Zermelo-Fraenkel "lite".
Introduction to numeralwise expressibility.
Goedel's incompleteness theorems.
An application of first-order logic to combinatorics.