On mathematical structure in a broad sense (Japanese)

For example, a ring is a structure of the language $\{+,-,\times,0,1\}$, and a ring is not a structure of the language $\{+,-,\times,\cdot^{-1},0,1\}$ because the domain of the operation $\cdot^{-1}$ of the multiplicative inverse is not the whole. In general, it is not officially possible to introduce a function symbol into a partial function. In this paper, we consider ``a structure in a broad sense'' that allows a partial function as the interpretation of a function symbol, we give its semantics and a Hilbert-style formal deductive system, and we prove the completeness theorem. Regarding sequent calculus and natural deduction, it may not be difficult, but it is an unsolved problem. ------ Intuitionistic logic, Kripke model, Universal TM, Derivability condition. (This is the Japanese version.)