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HU Credits:
4
Degree/Cycle:
1st degree (Bachelor)
Responsible Department:
Mathematics
Semester:
1st Semester
Teaching Languages:
Hebrew
Campus:
E. Safra
Course/Module Coordinator:
Prof. Itay Kaplan
Coordinator Office Hours:
by appointment
Teaching Staff:
Prof. Itay Kaplan,
Mr. George Peterzil
Course/Module description:
We will study basic concepts in mathematical logic. We will cover propositional calculus and predicate calculus (first order logic).
We will prove all the basic theorems (soundness, completeness, and compactness, both for propositional logic and for predicate logic).
We will describe a deduction system and prove its properties.
We will talk about some basic topics in model theory - complete theories, isomorphisms.
In the remaining time we will describe some connections between those topics and other areas of mathematics.
Course/Module aims:
The main goal of the course is to distinguish between syntax and semantics, and to study their connections.
Learning outcomes - On successful completion of this module, students should be able to:
The students will
1) distinguish between semantic and syntactic objects and recognize their connections,
2) define precisely the basic notions that we will introduce in class (proposition, formula, structure, connectives, quantifiers and others),
3) be able to prove theorems from class: properness, completeness, compactness.
4) be able to write a precise deduction using the deduction system presented in class.
5) know how to use "induction on the structure of the formula/sentence"
Attendance requirements(%):
0
Teaching arrangement and method of instruction:
Lecture + exercise
Course/Module Content:
Propositional calculus. Logical connectives. Truth tables.
Tautologies.
Complete set of connectives.
The compactness theorem for propositional logic.
The languages of predicate calculus (first order logic). Quantifiers.
Terms and formulas.
Free and bound variables.
Structures.
Satisfaction of formulas in structures.
The theory of a set of structures.
Models of a set of formulas.
Deductions.
The soundness theorem.
Godel’s completeness theorem.
The compactness theorem.
In the remaining time, we will touch on different subjects such as model theory and games.
We may learn more/other subjects.
Required Reading:
none
Additional Reading Material:
H. Enderton, A Mathematical Introduction to Logic
Grading Scheme :
Written / Oral / Practical Exam / Home Exam 85 %
Submission assignments during the semester: Exercises / Essays / Audits / Reports / Forum / Simulation / others 15 %
Additional information:
Lecture recordings will be available after each class.
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