Logic and Set Theory
- First-order predicate logic.
- Variables may represent domain objects, not
predicates or functions.
- No quantifiers over predicates or functions.
- Problem: "for all predicates p, ...", "there is a function
f, such that ..."
- First-order predicate logic over domain of sets.
- Domain objects are sets.
- May encode predicates and functions as sets.
- Interpret statements about sets as statements about predicates and
- Overcome limitations of first-order predicate logic.
The combination of first-order predicate logic and set theory is
the working horse of mathematics.
Author: Wolfgang Schreiner
Last Modification: October 14, 1999