# MATHEMATICAL LOGIC

Degree course:
Corso di Second cycle degree in MATHEMATICS
Academic year when starting the degree:
2016/2017
Year:
2
Academic year in which the course will be held:
2017/2018
Course type:
Compulsory subjects, characteristic of the class
Credits:
8
Period:
Second semester
Standard lectures hours:
80
Detail of lecture’s hours:
Lesson (80 hours)
Requirements:

No prerequisites are needed

Final Examination:
Orale

Oral examination

Assessment:
Voto Finale

Aims and outcomes
This is a traditional course in Mathematical Logic. Since classical logic and ZF set theory are the usual context to develop formal mathematical theories of any sort, the course aims at providing the tools to master all the involved notions, also by showing a number of examples. The last part introduces a few aspects of intuitionistic logic and constructive mathematics, to show how the study of logic is intimately related with the study of computable functions, i.e., computer programs. Also, the limits of logic and formal reasoning are explored in the presentation of the celebrated Goedel's incompleteness theorems.

Program
1. classical propositional logic: syntax, natural deduction calculus, semantics by means of truth tables and Boolean algebras, soundness, completeness

2. classical first-order logic: syntax, natural deduction calculus, Tarski's semantics, soundness, completeness, compactness

3. Zermelo-Fraenkel set theory: classes and sets, induction on sets, ordinals, cardinals, the axiom of choice, the continuum hypothesis

4. fundamentals of intuitionistic logic: syntax, algebraic propositional semantics (sketch), soundness, relation with computability (sketch)

5. limiting results: Goedel's incompleteness theorems

Notes

Frontal lectures

Intermediate assignments are available

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Degree course in: MATHEMATICS