4 papers
A 2-Categorical Bridge Between Henkin Constructions and Lawvere's Fixed-Point Theorem: Unifying Completeness and Compactness
Barreto Joaquim Reizi
We present a unified categorical framework that connects the syntactic Henkin construction for the first-order Completeness Theorem with Lawvere's Fixed-Point Theorem. Concretely,…
A Categorical Integration of Quantifiers:A Higher Category Theoretic Perspective
Barreto Joaquim Reizi
We propose a new framework for integrating quantifiers with other logical connectives in a higher-categorical setting. Our method systematically incorporates key coherence conditio…
A Categorical Integration of Logical Connectives via Higher Category Theory
Barreto Joaquim Reizi
This paper develops a systematic framework for integrating local categories that model logical connectives using higher category theory. By extending these local categories into a…
A Natural Homomorphism between the Model Constructions of the Completeness and Compactness Theorems
Barreto Joaquim Reizi
We establish a categorical framework relating two canonical model constructions in first-order logic: the Henkin construction and compactness-based constructions via ultraproducts…