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Single Idea 13656

[filed under theme 6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory ]

Full Idea

There are sets of natural numbers definable in set-theory but not in arithmetic.

Gist of Idea

Some sets of natural numbers are definable in set-theory but not in arithmetic

Source

Stewart Shapiro (Foundations without Foundationalism [1991], 5.3.3)

Book Ref

Shapiro,Stewart: 'Foundations without Foundationalism' [OUP 1991], p.123

Related Idea

Idea 13657 First-order arithmetic can't even represent basic number theory [Shapiro]