First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
MATHEMATICAL LOGIC
SCM0014417, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2015/16

Information on the course unit
Degree course First cycle degree in
MATHEMATICS
SC1159, Degree course structure A.Y. 2008/09, A.Y. 2017/18
N0
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Number of ECTS credits allocated 7.0
Type of assessment Mark
Course unit English denomination MATHEMATICAL LOGIC
Website of the academic structure http://matematica.scienze.unipd.it/2017/laurea
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction Italian
Branch PADOVA
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Lecturers
Teacher in charge MARIA EMILIA MAIETTI MAT/01

ECTS: details
Type Scientific-Disciplinary 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

Calendar
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)

Syllabus
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 proof-theoretic 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 Cerca nel catalogo
  • A. S. Troelstra and H. Schwichtenberg, Basic Proof Theory. --: Cambridge University Press, 1996. Cerca nel catalogo
  • Saunders Mac Lane, Categories for the Working Mathematician. --: Springer, 1978. Cerca nel catalogo