Mathematical Logic 1
A.Y. 2018/2019
Learning objectives
The courses have three aims.
First, teaching students how to reason using linear, intuitionistic, co-intuitionistic, and classical logic, and possibly the axiom of choice.
Second, familiarizing students with the way of thinking internal to category theory.
Third, showing some contemporary mathematical theories in action by means of the principles above.
First, teaching students how to reason using linear, intuitionistic, co-intuitionistic, and classical logic, and possibly the axiom of choice.
Second, familiarizing students with the way of thinking internal to category theory.
Third, showing some contemporary mathematical theories in action by means of the principles above.
Expected learning outcomes
Formalization abilities, use of a logical calculus, knowledge of the limits of logical mechanization.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
Elementary languages.
Tarski semantics for first order logic.
Theories and examples of theories.
Sequent calculus for classical logic (with some basic information on intuitionistic logic and
on cut elimination problems)
Completeness theorem for first order theories.
Hilbert calculi; formal systems for arithmetic.
Recursive functions and representability.
Goedelization techniques.
First Goedel incompleteness theorem.
Church theorem.
Tarski theorem.
Basic information on second Goedel incompleteness theorem.
Tarski semantics for first order logic.
Theories and examples of theories.
Sequent calculus for classical logic (with some basic information on intuitionistic logic and
on cut elimination problems)
Completeness theorem for first order theories.
Hilbert calculi; formal systems for arithmetic.
Recursive functions and representability.
Goedelization techniques.
First Goedel incompleteness theorem.
Church theorem.
Tarski theorem.
Basic information on second Goedel incompleteness theorem.
Professor(s)