Encoding sets as real numbers


© 2018 CEUR-WS. All rights reserved. We study a variant of the Ackermann encoding NA(x):= σ of the hereditarily finite sets by the natural numbers, applicable to the larger collection HF1/2 of the hereditarily finite hypersets. The proposed variation is obtained by simply placing a ‘minus’ sign before each exponent in the definition of NA resulting in the expression RA(x):= σ. By a careful analysis, we prove that the encoding RA is well-defined over the whole collection HF1/2 as it allows one to univocally assign a real-valued code to each hyperset in it. We also address some preliminary cases of the injectivity problem for RA.

CEUR Workshop Proceedings