Mathematical Logic I

Course Information
TitleΜΑΘΗΜΑΤΙΚΗ ΛΟΓΙΚΗ Ι / Mathematical Logic I
Code0133
FacultySciences
SchoolMathematics
Cycle / Level1st / Undergraduate, 2nd / Postgraduate
Teaching PeriodWinter
CommonYes
StatusActive
Course ID40000302

Programme of Study: Merikīs Foítīsīs (2014-sīmera)

Registered students: 1
OrientationAttendance TypeSemesterYearECTS
KORMOSElective Courses belonging to the selected specializationWinter-5.5

Programme of Study: UPS of School of Mathematics (2014-today)

Registered students: 86
OrientationAttendance TypeSemesterYearECTS
CoreElective Courses belonging to the selected specialization745.5
Class Information
Academic Year2025 – 2026
Class PeriodWinter
Faculty Instructors
Weekly Hours3
Total Hours39
Class ID
600276136
Type Of Offer
  • Disciplinary Course
Course Type 2021
Specialization / Direction
Course Type 2011-2015
Knowledge Deepening / Consolidation
Mode of Delivery
  • Face to face
Digital Course Content
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
  • Greek (Instruction, Examination)
  • English (Examination)
Prerequisites
Required Courses
  • 0102Α Introduction to Algebra and Number Theory
General Prerequisites
In the course "Mathematical Logic" we formalize and study Mathematical proofs. The interested students must have taken several courses that involve proofs.
Learning Outcomes
The students who successfully complete the course • have understood the notion of a formal first-order predicate language, its abilities and restrictions, with examples from known Mathematical theories. • can precisely define the notion of formal (Hilber-style) proofs • can distinguish between the semantical and syntantical aspects of Logic and can correlate them through the Theorems of Soundness and Completeness • can define "truth in a model" according to Tarski and can distinguish between "logical truths" (tautologies) and "mathematical truths" (axioms/theorems) which hold in the models of a certain theory.
General Competences
  • Apply knowledge in practice
  • Adapt to new situations
  • Make decisions
  • Work autonomously
  • Generate new research ideas
  • Advance free, creative and causative thinking
Course Content (Syllabus)
Propositional Calculus Formal language, Vocabulary, Connectives, Well-Formed Formulas, Truth assignments, Truth Tables, Logical Implications/Equivalences, Tautologies, Extra Connectives, Complete Set of Connectives, Boolean functions, Compactness Theorem, First-Order Predicate Calculus Formal Language, Vocabary, Formulas and Sentences, Models of a Formal Language, Truth- Evaluation in a Model, Logical Implication/Equivalence, Valid Formulas, Hilbert-style Proof Systems, Soundness and Completeness Theorems, Compactness Theorem and applications.
Keywords
Mathematical Logic, Propositional Calculus, First-order Predicate Calculus, Formal Proofs
Educational Material Types
  • Notes
  • Book
Use of Information and Communication Technologies
Use of ICT
  • Use of ICT in Course Teaching
  • Use of ICT in Communication with Students
Course Organization
ActivitiesWorkloadECTSIndividualTeamworkErasmus
Lectures39✓
Reading Assigment122✓✓✓
Exams4✓✓
Total165
Student Assessment
Description
There will be two midterm exams and a final exam. Grade is determined by weekly reading 10% midterm exams 25% x 2 final exam 40%
Student Assessment methods
  • Written Exam with Short Answer Questions (Formative, Summative)
  • Written Exam with Extended Answer Questions (Formative, Summative)
  • Written Exam with Problem Solving (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
- Μαθηματική Εισαγωγή στην Λογική, H. Enderton, Πανεπιστημιακές Εκδόσεις Κρήτης, 2013 Κωδικός Βιβλίου στον Εύδοξο: 32998373 ISBN: 9789605243999 - Μαθηματική λογική, Γ. Κολέτσος, Κάλλιπος, 2015 Διαθέσιμο δωρεάν: http://hdl.handle.net/11419/2299 Κωδικός Βιβλίου στον Εύδοξο: 320172 ISBN: 978-960-603-311-7 -Εισαγωγή στη Μαθηματική Λογική, Μάργαρης Αθανάσιος, Εκδόσεις Τζιόλα, 2017 Κωδικός Βιβλίου στον Εύδοξο: 50657752 ISBN: 9789604185290
Last Update
23-10-2025