Logical quantizations of first-order structures
The paper is part of a long series of articles (published in Int. J. Theor. Phys., Vol. 31-35), concerning quantization of various mathematical structures. In this paper quantization of mathematical structures defined by so called limit theories is considered (including, e.g., posets and order-preserving mappings, or Banach spaces and contractive linear transformations). The author works with infinitary many-sorted first-order logics. Category theory is also used essentially. The paper is sufficiently characterized by an outline of the content, due to the author himself: ``Section 1 is devoted to a review of infinitary logic, sketches, accessible categories \dots . After limit sketches are Booleanized in Section 2, the relationship between two Booleanizations of limit sketches \dots is discussed in Section 3. The last section is devoted to quantizing limit sketches logically''.
infinitary many-sorted first-order logics
scientific article; zbMATH DE number 889797
scientific article