Set Theory and Logic

Information Curvature, Completed Infinity, and a Proposed Route to Inconsistency in ZFC

Authors: Steven E. Elliott
Comments: 7 Pages.

This paper proposes an information-curvature critique of the classical set-theoretic treatment of completed infinity. For finite sets, cardinal growth under powerset formation corresponds to a strict decrease in reciprocal cardinality. We define finite information curvature and finite super-curvature by

s(X) = 1/|X|,     S(X) = 1/|P(X)|.

For finite sets, |X| < |P(X)| if and only if s(X) > s(P(X)). As finite sets exhaust an infinite process, both curvature and super-curvature tend to zero.

This paper does not claim to exhibit a completed formal contradiction inside ZFC. Instead, it isolates a proposed route to such a contradiction: Cantorian set theory asserts strict hierarchies of completed infinities, while finite-observational information curvature collapses the corresponding residual distinction to zero. The central hypothesis is that the logical tension arises from treating completed infinity as a coherent object. The proposed replacement is a zero-curvature flat-infinity axiom: an infinite information set N satisfies |N| = |P(N)|, so powerset formation does not generate a higher completed cardinal layer at the zero-curvature limit.

Category: Set Theory and Logic