Marco Benini

Mathematical Logic

Program
  • Propositional logic: language, deduction system, semantics, soundness, completeness;
  • First-order logic: syntax, semantics, soundness, completeness, compactness;
  • Set theory: fundamental axioms, ordinals, cardinals, transfinite induction, axiom of choice, continuum hypothesis;
  • Constructive mathematics: intuitionistic logic, computable functions, λ-calculi, propositions as types;
  • Limiting results: Peano arithmetic, Gödel’s incompleteness theorems, natural incompleteness results, incompleteness and computability.

The slides of the course are available: select the right academic year

Here are some exercises on natural deduction.

The textbook is still under development: a first draft is available for inspection.

Assignments
date text solution
7 nov 2016 pdf pdf
5 dec 2016 pdf pdf
16/17 jan 2017 pdf pdf
1 feb 2017 pdf pdf

Results (academic year 2016/17)

Surname (first letter) Name (first letter) First assignment Second assignment Third assignment Fourth assignment Final result
A L 25 20 24 25 24
D C 26 20 35 32 28
L G 36 32 36 30 30+
P A 16 20
R E 30 12 34 26 26
S J 34 34 36 34 30+
Z M 24 28 28 34 29