Article citationsMore>>

Cohen, P.J. (1963) The Independence of the Continuum Hypothesis. Proceedings of the National Academy of Sciences of the United States of America, 50, 1143-1148.
https://doi.org/10.1073/pnas.50.6.1143

has been cited by the following article:

• TITLE: The Infinity Tree: Representing Infinities of Real Numbers with Countably Infinite Tree Structures

  AUTHORS: Philip C. Jackson

  KEYWORDS: Infinity, Countable, Diagonalization, Real Numbers, Tree Structure, Infinity Tree, Continuum Hypothesis

  JOURNAL NAME: Advances in Pure Mathematics, Vol.13 No.4, April 28, 2023

  ABSTRACT: This paper discusses how the infinite set of real numbers between 0 and 1 could be represented by a countably infinite tree structure which would avoid Cantor’s diagonalization argument that the set of real numbers is not countably infinite. Likewise, countably infinite tree structures could represent all real numbers, and all points in any number of dimensions in multi-dimensional spaces. The objective of this paper is not to overturn previous research based on Cantor’s argument, but to suggest that this situation may be treated as a definitional or axiomatic choice. This paper proposes a “non-Cantorian” branch of cardinality theory, representing all these infinities with countably infinite tree structures. This approach would be consistent with the Continuum Hypothesis.