Several problems that pertain to certain arithmetically well-behaved countable subsemirings of Λ, the semiring of isols, are discussed. This is relevant to the present volume memorializing the late John Myhill, in that Myhill was an early co-developer of the theory of Λ.

Hirschfeld and Wheeler proved in 1975 that ∑1 ultrapowers (= “simple models”) are rigid; i.e., they admit no non-trivial automorphisms. We later noted, essentially mimicking their technique, that the same is true of Δ1 ultrapowers (= “Nerode semirings”), a class of models of Π2 Arithmetic that overlaps, but is mutually non-inclusive with, the class of Σ1 ultrapowers. Hirschfeld and Wheeler left as open the question whether some Σ1 ultrapowers might admit proper isomorphic self-injections. We do not answer that question; but (...) we do answer the corresponding question, in the negative, for the Δ1 case. (shrink)

At all times, the book was understood not only as a means of preserving and transforming knowledge, but also as a means of knowing the world around us. At the same time, from ancient times it was a subject of knowledge. Gradually its theoretical phenomenon was formed. The book essentially is the most important form of consolidation and transfer of information in space and time. From the point of view of the theory of communication, the book serves as one of (...) the forms of existence and dissemination of semantic information, a means of organizing the work of individual consciousness into a sign system for the perception of its social consciousness. After all, the evolution of the book is inextricably linked with the history of mankind. She is the foundation on which the culture of peoples is built. It helps society to grow and improve, borrow and use all the mass of knowledge accumulated by mankind. The book is the most complete and comprehensive expression of the spiritual culture of mankind, since its origin and development are inextricably linked with it. (shrink)

The study of the formation of the literary culture of the words of the "peoples of the nations" is impossible without analyzing the role of libraries of monasteries and cathedrals as centers of documentary memory of the Christian past. After all, the library, as a social institution, has always played an important role in the development of education, science, culture, and religious thought on a long path to its development.

While ante rem structuralism offers a promising account of mathematical truth and mathematical ontology, several of the most prominent formulations of the view seem to be subject to significant difficulties involving the identity conditions of the objects they posit. In this paper I argue that those difficulties can be overcome by adopting encoding structuralism, a version of realism about mathematical objects developed by Bernard Linsky, Uri Nodelman and Edward Zalta.

I. Wesen und entwicklung des humanitätsgedankens.--II. Der socialismus.--III. Der individualismus.--IV. Der utilitarianismus.--V. Der pessimismus.--VI. Der evolutionismus.--VII. Der positivismus.--VIII. Nietzsches uebermensch.--IX. Die hauptgrundsätze einer modernen humanitätsethik.