English

Finite Sets and Counting

History and Overview 2010-06-22 v2

Abstract

We start by presenting a theory of finite sets using the approach which is essentially that taken by Whitehead and Russell in Principia Mathematica}, and which does not involve the natural numbers (or any other infinite set). This theory is then applied to prove results about structures which, like the natural numbers, satisfy the principle of mathematical induction, but do not necessarily satisfy the remaining Peano axioms.

Keywords

Cite

@article{arxiv.0809.0105,
  title  = {Finite Sets and Counting},
  author = {Chris Preston},
  journal= {arXiv preprint arXiv:0809.0105},
  year   = {2010}
}

Comments

55 pages

R2 v1 2026-06-21T11:15:23.753Z