Modern Logic — A Survey pp 167-171 | Cite as

# Logic and Set Theory

## Abstract

In mathematics, our formation of sets is quite often of the form ‘the set of all satisfying *x* certain property’. Since logic is the calculus about the property, the nature of logic plays an intrinsic role in set theory. Here we take the classical logic, the intuitionistic logic, and the quantum logic and discuss the relation between each of them and set theory. Let us say a few words on these logic. The classical logic is the logic of the absolute. The intuitionistic logic is the logic of the mind. The quantum logic is the logic of the particles. The precise definition of the quantum logic is the logic of the closed linear subspaces of a Hilbert space.

## Preview

Unable to display preview. Download preview PDF.

## Bibliography

- [1]M. Davis, ‘Takeuti Models and Foundations of Quantum Mechanics’, A talk given at Symposium on Abraham Robinson’s theory of infinitesimal, Iowa City, 1977.Google Scholar
- [2]R. Grayson, ‘A Sheaf Approach to Models of Set Theory’, Master thesis, Oxford, 1975.Google Scholar
- [3]T. Jech,
*Lectures in Set Theory*, Lectures Notes in Mathematics No. 217, Springer, 1971.Google Scholar - [4]D. Scott, ‘Boolean Valued Models and Non-Standard Analysis’, in
*Applications of Model Theory to Algebra, Analysis and Probability*, Holt, Reinhart and Winston, 1969.Google Scholar - [5]G. Takeuti,
*Two Applications of Logic to Mathematics*, Publications of the Mathematical Society of Japan No. 13, Iwanami and Princeton University Press, 1978.Google Scholar - [6]G. Takeuti, ‘Boolean Valued Analysis’,
*Applications of Sheaves*, Edited by Fourman, Mulvey, and Scott, Lecture Notes in Mathematics No. 753, Springer, 1979.Google Scholar - [7]G. Takeuti and W. Zaring,
*Axiomatic Set Theory*, Springer, 1973.Google Scholar