
Course unit
MATHEMATICAL LOGIC
SCM0014417, A.A. 2017/18
Information concerning the students who enrolled in A.Y. 2015/16
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
MAT/01 
Mathematical Logic 
7.0 
Mode of delivery (when and how)
Period 
First semester 
Year 
3rd Year 
Teaching method 
frontal 
Organisation of didactics
Type of hours 
Credits 
Hours of teaching 
Hours of Individual study 
Shifts 
Practice 
4.0 
32 
68.0 
No turn 
Lecture 
3.0 
24 
51.0 
No turn 
Start of activities 
02/10/2017 
End of activities 
19/01/2018 
Examination board
Board 
From 
To 
Members of the board 
6 Logica Matematica  2017/2018 
01/10/2017 
30/09/2018 
MAIETTI
MARIA EMILIA
(Presidente)
SAMBIN
GIOVANNI
(Membro Effettivo)
CIRAULO
FRANCESCO
(Supplente)
MASCHIO
SAMUELE
(Supplente)

Prerequisites:

some basic knowledge of algebra and topology. 
Target skills and knowledge:

The aim of the course in logic is to study the relation between syntax and semantics of a formal language and to illustrate the main properties of logical calculi and their main expressive and prooftheoretic limits. 
Examination methods:

written with the possibility to add an oral examination 
Assessment criteria:

the aim of the exam is to evaluate the knowledge of the student on the topics of the corse 
Course unit contents:

This course is about the study of the expressive power and corresponding limits of deductive formal systems for both classical and intuitionistic predicate logics as well as for their corresponding extensions with Peano axioms of arithmetic.
We will study
decision procedures for their propositional fragments,
semidecision procedures for the full predicate logics,
the main theorems about the equivalence between the mentioned logics and their algebraic semantics,
Goedel incompleteness theorems for both classical and intuitionistic arithmetic. 
Planned learning activities and teaching methods:

Classroom lessons 
Additional notes about suggested reading:

Notes provided by the lecturer 
Textbooks (and optional supplementary readings) 

Dirk van Dalen, Logic and structure. London: Springer, 2012. 5th revised, extended edition

A. S. Troelstra and H. Schwichtenberg, Basic Proof Theory. : Cambridge University Press, 1996.

Saunders Mac Lane, Categories for the Working Mathematician. : Springer, 1978.


