Diophantine correct models of arithmetic

Arithmetic and Diophantine Geometry

Diophantine undecidable theories of arithmetic

1 Diophantine undecidability Let T be a theory in the usual rst-order language of arithmetic L A (with non-logical symbols 0; 1; +; ; <) extending PA ? , the theory of the nonnegative parts of discretely ordered rings. I shall make use of the usual classes of L A-formulas deened in terms of quantiier complexity, 9 1 1 is the set of L A-formulas of the form 9 x (x; y) with quantiier-free, and 1 ...

Diophantine Equations Involving Arithmetic Functions of Factorials

DIOPHANTINE EQUATIONS INVOLVING ARITHMETIC FUNCTIONS OF FACTORIALS Daniel M. Baczkowski We examine and classify the solutions to certain Diophantine equations involving factorials and some well known arithmetic functions. F. Luca has showed that there are finitely many solutions to the equation:

Diophantine Equations, Presburger Arithmetic and Finite Automata

We show that the use of nite automata provides a decision procedure for Presburger Arithmetic with optimal worst case complexity.

Diophantine Approximation with Arithmetic Functions, Ii

We prove that real numbers can be well-approximated by the normalized Fourier coefficients of newforms.