Author’s Modality of Didactic Text and Reader’s Perception (by Example of A. G. Dymov’s “Adab”)

Aspects of the author’s modality manifestation and related features of didactic text perception are considered. The authors briefly describe the reflection of didactic discourse in the literary reception, argue the importance of identifying the author’s modality in the moralizing texts presented in the educational literature. Based on a specific material, the authors study the forms of expression of the author’s consciousness and the specifics of perception of the didactic text. The defining role of background knowledge in a situation when the reader and the author of a didactic work belong to different eras is shown. Expressions of modality in the present article are determined by the choice of genre and interaction between the author’s consciousness with the laws of the genre, points of view dominant in the text and the regularities of their interactions, the choice of character and characters, the degree of categoricity of the author’s “I.” Examples are given from the didactic works of A. G. Dymov (“Adab”), whose work has not yet been considered from the position of semantic expressiveness of the subject of the author’s plan involved in it. Despite the fact that the measure of subjectivity in a didactic text intended for educational purposes should be minimal, and their aesthetics can be unassuming, it is proved on a specific material that the recognition of forms of author’s modality allows not only to specify the author’s value attitudes, but also to judge in many ways the reasons that hold attention when reading such texts.

Coding in the automorphism group of a computably categorical structure

Using new techniques for controlling the categoricity spectrum of a structure, we construct a structure with degree of categoricity but infinite spectral dimension, answering a question of Bazhenov, Kalimullin and Yamaleev. Using the same techniques, we construct a computably categorical structure of non-computable Scott rank.

DEGREES OF CATEGORICITY AND SPECTRAL DIMENSION

A Turing degreedis the degree of categoricity of a computable structure${\cal S}$ifdis the least degree capable of computing isomorphisms among arbitrary computable copies of${\cal S}$. A degreedis the strong degree of categoricity of${\cal S}$ifdis the degree of categoricity of${\cal S}$, and there are computable copies${\cal A}$and${\cal B}$of${\cal S}$such that every isomorphism from${\cal A}$onto${\cal B}$computesd. In this paper, we build a c.e. degreedand a computable rigid structure${\cal M}$such thatdis the degree of categoricity of${\cal M}$, butdis not the strong degree of categoricity of${\cal M}$. This solves the open problem of Fokina, Kalimullin, and Miller [13].For a computable structure${\cal S}$, we introduce the notion of the spectral dimension of${\cal S}$, which gives a quantitative characteristic of the degree of categoricity of${\cal S}$. We prove that for a nonzero natural numberN, there is a computable rigid structure${\cal M}$such that$0\prime$is the degree of categoricity of${\cal M}$, and the spectral dimension of${\cal M}$is equal toN.

DEGREES OF CATEGORICITY ON A CONE VIAη-SYSTEMS

We investigate the complexity of isomorphisms of computable structures on cones in the Turing degrees. We show that, on a cone, every structure has a strong degree of categoricity, and that degree of categoricity is${\rm{\Delta }}_\alpha ^0 $-complete for someα. To prove this, we extend Montalbán’sη-system framework to deal with limit ordinals in a more general way. We also show that, for any fixed computable structure, there is an ordinalαand a cone in the Turing degrees such that the exact complexity of computing an isomorphism between the given structure and another copy${\cal B}$in the cone is a c.e. degree in${\rm{\Delta }}_\alpha ^0\left( {\cal B} \right)$. In each of our theorems the cone in question is clearly described in the beginning of the proof, so it is easy to see how the theorems can be viewed as general theorems with certain effectiveness conditions.