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A Formalization of Set Theory without Variables
About this Title
Alfred Tarski and Steven Givant
Publication: Colloquium Publications
Publication Year:
1987; Volume 41
ISBNs: 978-0-8218-1041-5 (print); 978-1-4704-3187-7 (online)
DOI: https://doi.org/10.1090/coll/041
MathSciNet review: MR920815
MSC: Primary 03B30; Secondary 03C05, 03E30, 03G15
Table of Contents
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Front/Back Matter
Chapters
- Chapter 1. The formalism $\mathcal L$of predicate logic
- Chapter 2. The formalism $\mathcal L^+$, a definitional extension of $\mathcal L$
- Chapter 3. The formalism $\mathcal L^+$ without variables and the problem of its equipollence with $\mathcal L$
- Chapter 4. The relative equipollence of $\mathcal L$ and $\mathcal L^+$, and the formalization of set theory in $\mathcal L^\times$
- Chapter 5. Some improvements of the equipollence results
- Chapter 6. Implications of the main results for semantic and axiomatic foundations of set theory
- Chapter 7. Extension of results to arbitrary formalisms of predicate logic, and applications to the formalization of the arithmetics of natural and real numbers
- Chapter 8. Applications to relation algebras and to varieties of algebras