Presburger Arithmetic

Presburger Arithmetic is a simplified version of number theory focused on the properties of natural numbers using addition. It allows statements about numbers and their sums but does not include multiplication. Developed by Mojżesz Presburger in the 1920s, this system is notable because it can definitively decide whether any given statement about the numbers is true or false. This contrasts with standard arithmetic, where some questions remain unsolvable. Presburger Arithmetic has applications in computer science, particularly in logic, verification, and computational mathematics, providing a foundation for understanding more complex systems without multiplication.