# INTRODUCTION TO LOGIC AND SET THEORY

### Lecturers

• Dr. Ivgenya Ackermann
• Office: Mathematics Building, Room -120
• Office hours: Sunday 14-16

• Prof. Ido Efrat
• Office: Mathematics Room 106
• Office hours: Sunday 14-16
• Tel.: (08) 6461627
• e-mail: efrat@math.bgu.ac.il

• Dr. Ruvim Lipyansky
• Office: Mathematics Building, Room -104
• Office hours: Wednesday 14-16
• Tel.: (08) 6477805
• e-mail: lipyansk@math.bgu.ac.il

## Teaching Assistants

• Amir Gurion
• Office: Mathematics Building, Room 129
• Office hours: TBA

• Victoria Lubitch
• Office: Mathematics Building, Room 127
• Office hours: TBA

• Yona Meisel
• Office: Mathematics Building, Room 129
• Office hours: TBA

### Expected Course Syllabus

#### Part I: Basic notions in set Theory

Sets, set operations, relations, equivalence relations and partitions, partial and total orderings, the natural numbers, induction principles, functions

#### Part II: Propositional Calculus

Truth tables, truth values, logical equivalence, disjunctive normal forms, complete connector systems

#### Part III: Predicate Calculus

Its language, formulas, structures, satisfaction, normal forms, definability, isomorphisms of structures

#### Part IV: Cardinal Arithmetic

bijections, cardinal numbers and equi-cardinality, the Cantor-Bernstein theorem, |A|<|P(A)|, cardinal arithmetic, fundamental examples (Q, R, P(N), ...), the diagonalization argument, countable sets, Zorn's lemma and the Axiom of choice

### Exercises

Exercise 1 (ps) (pdf)

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Exercise 2 (ps) (pdf) (jpg)

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Exercise 3 (ps) (pdf) (jpg)

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Exercise 4 (ps) (pdf) (gif - page 1) (gif - page2)

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Exercise 5 (ps) (pdf)

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Exercise 6 (jpg)

Exercise 7 (ps) (pdf)

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Exercise 8 (ps) (jpg)

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Exercise 9 (ps) (pdf)

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Exercise 10 (ps) (pdf)

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Exercise 11 (ps) (jpg)

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Exercise 12 (jpg)

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