Hyperfinite and standard unifications for physical theories
If \(L\) denotes a nonempty language, \(\mathcal P\) the power operator, and \(\mathcal F\) the finite power set operator, then a mapping \(\mathcal C: \mathcal P(L)\to\mathcal P(L)\) is called a general consequence operator or closure operator in the sense of Tarski if for each \(X,Y\in\mathcal P(L)\), (i) \(X\subset\mathcal C(X)=\mathcal C(\mathcal C(X))\subset L\); and if (ii) \(X\subset Y\), then \(\mathcal C(X)\subset\mathcal C(Y)\). \(\mathcal C\) is called finitary if (iii) \(\mathcal C(X)=\bigcup\{\mathcal C(A)\mid A\in\mathcal F(X)\}\). In this paper the author shows, among other things, that certain physical theories can be represented by a nonempty subset \(\{S_{N_j}^V \mid j\in\mathbb N\}\) of the lattice \(\mathcal C(\Lambda)\) of consequence operators on a language \(\Lambda\).
scientific article; zbMATH DE number 1751290