Nikitin's Theorem II: Probabilistic Realization of Logically Impossible Events via Model-Theoretic Extensions

DescriptionThis work presents Nikitin’s Theorem II, a new result at the intersection of probability theory and mathematical logic. The theorem establishes that events which are logically impossible within a given consistent formal system can become almost-surely realizable in a suitably constructed limit model. The proof combines three classical components: A weighted generalization of the Borel–Cantelli lemma for dependent events, The Model-Theoretic Compactness Theorem, A memory-weighted forcing scheme controlling dependence decay. By applying a divergent weighted probability criterion across an ascending ladder of model extensions, the theorem demonstrates a rigorous probabilistic mechanism for transitioning from logical impossibility to almost-sure realization. This unifies probabilistic inevitability with model-theoretic expansion and has potential applications in probabilistic metamathematics, epistemic logic under uncertainty, and iterative model-building in artificial intelligence.