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arXiv · 2503.06091

Theta Theory: operads and coloring

Matilde Marcolli·Richard K. Larson
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Abstract

We give an explicit construction of the generating set of a colored operad that implements theta theory in the mathematical model of Minimalism in generative linguistics, in the form of a coloring algorithm for syntactic objects. We show that the coproduct operation on workspaces allows for a recursive implementation of the theta criterion. We also show that this filtering by coloring rules on structures freely formed by Merge is equivalent to a process of structure formation by a colored version of Merge: the form of the generators of the colored operad then implies the dichotomy is semantics between External and Internal Merge, where Internal Merge only moves to non-theta positions.

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Matilde Marcolli, Richard K. Larson. 2025-03-08. Theta Theory: operads and coloring. https://arxiv.org/abs/2503.06091

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