Logische technieken 2001 (Logical Techniques)

• Week 1; Recapitulation natural deduction for propositional logic. Introduction of predicate logic with its syntax and a natural deduction system for it. Treatment of inductive proofs, applied to the natural numbers and to inductive structures in general, like formulas, terms, proofs, et cetera. Tarski's Truth definition.
  
• Week 2;
  Semantics for first order logic. Some model theoretic notions: equivalence relation, congruence relation, homomorphism, isomorphism. Some constructions with f.o. models: cartesian product and quotient. Applications: Chinese remainder theorem, construction of the integers out of the positive integers, construction of the rationals out of the integers.
• Week 3;
  The completeness theorem for first order predicate logic; Henkin construction. Applications of the compactness theorem. k-colorability of a graph. The principle of overflow.
• Week 4;
  
• Week 5;
  
• Week 6;