Article · Mathematical Notes · April 1, 2025
Pseudo-Countably-Categorical Formulas and Theories
B. Sh. Kulpeshov, In. I. Pavlyuk, Sergey Vladimirovich Sudoplatov
Abstract
Abstract The concept of a pseudo-countably-categorical formula is introduced, and the syntactic and semantic possibilities of such formulas are investigated. Approximations of theories using such formulas, including pseudo-countably-categorical ordered theories, theories of Abelian groups and modules, and Ehrenfeucht theories, are studied. A description of canonical representatives of pseudo-countably-categorical ordered theories is given. The preservation and violation of pseudo-countable categoricity under expansions and restrictions of theories are considered. Countable spectra of pseudo-countably-categorical theories are described.
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