[FOM] Imaginary numbers in logic -- answer to Jim

José Félix Costa fgc at math.ist.utl.pt
Fri Dec 2 04:23:40 EST 2005

That some aspects of the dynamics of complex numbers can be imagined WITHOUT
the square root of -1 (or of -15 in Mazur's book) is well know in
Mathematical Logic, e.g., in the study of Diophantine equations.

Insights can be found in Martin Davis's celebrated book in Dover (namely in
Appendix 2) and in Bell & Machover's chapter 6 on Recursion Function Theory
(Mathematical Logic, North-Holland): intuitions are given when analising the
class of solutions of the so called Pell's equation.

Galois Theory can also be visited to study the group of solutions of a
particular Diophantine equation.

J  Felix

J. Felix Costa
Departamento de Matematica
Instituto Superior Tecnico
Av. Rovisco Pais, 1049-001 Lisboa, PORTUGAL
tel:      351 - 21 - 841 71 45
fax:     351 - 21 - 841 75 98
e-mail:   fgc at math.ist.utl.pt
www:    http://fgc.math.ist.utl.pt/jfc.htm

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