Sets, Logic, and Mathematical Foundations
Lectures given at a Summer Institute for Teachers of Secondary and College Mathematics, sponsored by the National Scienc
136 2 31MB
English Pages [175] Year 1956
Table of contents :
Title Page
Corrections and Emendations
Chapter I: Sets
1 Sets and elements
2 Subsets of a given set
3 Countable and uncountable sets
4 Cardinal number
5 The paradoxes
6 Axiomatic set theory
Chapter II: Logic
7. The propositional calculus (model theory): validity
8. The propositional calculus (model theory): valid consequence
9. The propositional calculus (proof theory): provability and decidability
10. The predicate calculus (model theory): validity
11. The predicate calculus (model theory): valid consequence
12. The predicate calculus (proof theory): provability and deducibility
Chapter III: Mathematical Foundations
13. Axiomatic thinking vs. intuitive thinking in mathematics
14. Formal systems, metamathematics
15. Turing machines, Church's thesis
16. Church's theorem
17. Gödel's theorem
18. Gödel's theorem and Skolem models
(end)
Title Page
Corrections and Emendations
Chapter I: Sets
1 Sets and elements
2 Subsets of a given set
3 Countable and uncountable sets
4 Cardinal number
5 The paradoxes
6 Axiomatic set theory
Chapter II: Logic
7. The propositional calculus (model theory): validity
8. The propositional calculus (model theory): valid consequence
9. The propositional calculus (proof theory): provability and decidability
10. The predicate calculus (model theory): validity
11. The predicate calculus (model theory): valid consequence
12. The predicate calculus (proof theory): provability and deducibility
Chapter III: Mathematical Foundations
13. Axiomatic thinking vs. intuitive thinking in mathematics
14. Formal systems, metamathematics
15. Turing machines, Church's thesis
16. Church's theorem
17. Gödel's theorem
18. Gödel's theorem and Skolem models
(end)
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