Varieties of Infiniteness in the Existence of Infinitely Many Primes

Victor Pambuccian ()
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Victor Pambuccian: Arizona State University - West Campus, School of Mathematical and Natural Sciences

Chapter Chapter 7 in Axiomatic Thinking II, 2022, pp 157-164 from Springer

Abstract: Abstract By providing quantifier-free axioms systems, without any form of induction, for a slight variation of Euclid’s proof and for the Goldbach proof for the existence of infinitely many primes, we highlight the fact that there are two distinct and very likely incompatible concepts of infiniteness that are part of the theorems proved. One of them is the concept of cofinality, the other is the concept of equinumerosity with the universe.

Date: 2022
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DOI: 10.1007/978-3-030-77799-9_7

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