A Peculiar Subset of The Smallest Inductive Set

EasyChair Preprint no. 2113

Abstract

By ZF, there exists a peculiar subset \bar{ω} of the smallest inductive set ω, which is not just infinite, but D-finite. If ZF is consistent, then ZF+ \bar{ω} \not= ω is also consistent; otherwise, ZF is inconsistent. Moreover, if ZF is consistent, then \bar{ω} and ω are indistinguishable in the forcing method, and so the forcing method has limitation. In order to avoid conflicts with ZF, it will be necessary to discriminate \bar{ω} from ω in the forcing method, and thus some problems relevant to \bar{ω} deserve deeper discussion.

Keyphrases: Axioms of Zermelo-Fraenkel, CH, D-finite, Forcing method, Gonsistency, the peculiar subset of the smallest inductive set infinite, The smallest inductive set

@Booklet{EasyChair:2113,
  author = {Feng Zhao},
  title = {A Peculiar Subset of The Smallest Inductive Set},
  howpublished = {EasyChair Preprint no. 2113},

  year = {EasyChair, 2019}}