Definability of arithmetical operations from binary quadratic forms. (English) Zbl 1024.03011

The author shows that some binary quadratic forms \(F_{a,b,c}(x,y)=ax^2+bxy+cy^2\) are def-complete, i.e. they suffice to define addition and multiplication on the set \(\mathbb N\) of nonnegative integers.


03B25 Decidability of theories and sets of sentences
11C99 Polynomials and matrices
03B10 Classical first-order logic
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