Exact anti-types in first-order relational anti-algebraic structures

2026

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DOI 10.70474/1rr6xg74
Data confidence 70 medium
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Abstract

We introduce a first-order relational framework for anti-algebraic structures inspired by neutrosophic anti-groups. We formalize anti-axioms corresponding to the negation of classical group properties, analyze their logical dependencies, and provide a complete classification of realizable anti-types. In particular, we show that there exist exactly 20 distinct anti-types, each realized by a finite structure. Connections with hypergraph theory and combinatorics are also discussed.