Primitively Recursive Categoricity for Unars and Equivalence Structures
K. V. Blinov · Siberian Mathematical Journal · 2021
This continues the study of the primitively recursive categoricity of structures for which there exists a primitively recursive decision algorithm with witnesses of all $ \Sigma $ -formulas. Considering the equivalence structures, we find a complete criterion for primitively recursive categoricity over the class $ K_{\Sigma} $ , which coincides with the already known criterion for computable categoricity. As regards unars, the structures with one arbitrary unary function, we distinguish some conditions for primitively recursive categoricity over $ K_{\Sigma} $ and also for the absence of this categoricity. In particular, we find a full description of primitively recursive injective unars categorical over $ K_{\Sigma} $ .