The accelerated introduction of digital technologies in education has already acquired an avalanche-like mode, which has become an effective factor in research to improve the conceptual and technological solutions for the development and application of various synthetic learning environments. One of the most important areas of their improvement is giving them flexibility to maximize the capabilities of each student. In the theory and practice of psychology, this route is associated with various

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... options for implementing the personal approach as a personalization of learning. Engineering and communication technologies in education open up opportunities for personalizing learning, which have expanded significantly, but the problems of theory and practice of education have also become more relevant. Various options for personalization of training are also implemented when creating synthetic artificial environments, one of the actively developed varieties of which are adaptive learning systems (ALS). The main factors that complicate the use of ALS, experts attribute their high cost and insufficient efficiency, which necessitates the search for new approaches to the development of ALS on the most clear, rational theoretical and methodological principles. Also, the reason for the limited use of ALS is that the personalization inherent in their design does not allow for the necessary consideration the shades of students' socio-psychological specifics in combination with regulatory requirements, which teachers achieve by developing and implementing their training programs.Conceptually, research on ALS is an example of the interacting the natural science and humanitarian paradigms in human studies. To increase the effectiveness of such interaction, logically relevant theoretical models are needed that are applicable to a wide range of subjects studied within the framework of the humanitarian paradigm. Such a theoretical model for the description and development of ALS, in particular, can be built on the basis of the set-theoretic method for process description. The article deals with the application of this method to the structure and functioning of the ALS and the implementation of the adaptation principle in it.