Chapter 5 from the book

"HILBERT's TENTH PROBLEM"

Section 5.7 .html
Commentary .html
Chapter 5 .ps.gz

Sections 5.1 and 5.2 can be read without reading previous chapters in advance.

For reading Sections 5.3 and 5.4, it is sufficient to know that functions Cantor and Cantor_n are defined in Section 3.3 in the following way:

Cantor(a,b)=( (a+b)²+ 3a+b)/2,

Cantor₁(a₁)=a₁,

Cantor_n+1(a₁, ..., a_n+1)= Cantor_n(a₁, ..., a_n-1, Cantor(a_n, a_n+1))

and that function Cantor_n maps one-to-one Nⁿ onto N, where N is the set of non-negative integers.

The English translation of Chapter 5 is placed on WWW with kind permition of The MIT Press.