TITLE:
About the Strange Tree Paradox and Possible Inconsistency of Set Theory
AUTHORS:
Yury M. Volin
KEYWORDS:
Set Theory, Inconsistency, Tree, Strange Tree, Through Way, Almost Through Way, Isomorphism, Almost Isomorphism
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.13 No.10,
October
31,
2023
ABSTRACT: The existence of “strange trees” is proven and their paradoxical nature is discussed, due to which set theory is suspected of being contradictory. All proofs rely on informal set-theoretic reasoning, but without using elements that were prohibited in axiomatic set theories in order to overcome the difficulties encountered by Cantor’s naive set theory. Therefore, in fact, the article deals with the possible inconsistency of existing axiomatic set theories, in particular, the ZFC theory. Strange trees appear when uncountable cardinals appear.