On mathematical structure in a broad sense (Japanese)

Hiroki Yagisita
<span title="2020-09-23">2020</span> <i title="Zenodo"> Zenodo </i> &nbsp;
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
more &raquo; ... 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. (This is the Japanese version.)
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