Arithmetic in Peano Arithmetic

Lorenz Halbeisen and Regula Krapf
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Lorenz Halbeisen: ETH Zurich, Department of Mathematics
Regula Krapf: Universität Bonn, Mathematics Institute

Chapter Chapter 8 in Gödel's Theorems and Zermelo's Axioms, 2025, pp 91-101 from Springer

Abstract: Abstract In this chapter, we take a closer look at Peano Arithmetic (PA) which we have defined in Chapter 1. In particular, we prove within PA some basic arithmetical results, starting with the commutativity and associativity of addition and multiplication, culminating in some results about coprimality. This paves the way for the coding of finite sequences of numbers, which will be covered in the next chapter.

Date: 2025
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DOI: 10.1007/978-3-031-85106-3_9

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