4 papers · 1 filter
On the Nature of Fractal Numbers and the Classical Continuum Hypothesis (CH)
Stanislav Semenov
We propose a reinterpretation of the continuum grounded in the stratified structure of definability rather than classical cardinality. In this framework, a real number is not an ab…
Fractal Origin of the Continuum: A Hypothesis on Process-Relative Definability
Stanislav Semenov
We propose a new constructive model of the real continuum based on the notion of fractal definability. Rather than assuming the continuum as a completed uncountable totality, we vi…
Fractal Countability as a Constructive Alternative to the Power Set of N: A Meta-Formal Approach to Stratified Definability
Stanislav Semenov
Classical set theory constructs the continuum via the power set P(N), thereby postulating an uncountable totality. However, constructive and computability-based approaches reveal t…
Constructive Limits of Cantor's Diagonal Method: Countability, Enumerability, and the Impossibility of Exhausting the Continuum
Stanislav Semenov
Cantor's diagonal method is traditionally used to prove the uncountability of the set of all infinite binary sequences. This paper analyzes the expressive limits of this method. It…