Form equivalence class Howard-Rubin Number: 1
Statement: Every partial function on a set \(A\) can bedefined as follows: Let \(\varrho\), \(\sigma\), \(\varphi\), \(\tau_1\),\(\tau_2\), \(\tau_3\) be equivalence relations on \(A\) such that \(\sigma\)has a distinguished equivalence class \(D\) which is a set of distinctrepresentatives for the equivalence classes of \(\varrho\), \(\varphi\)has at most three equivalence classes \(D_1\), \(D_2\), and \(D_3\), andthe equivalence classes of \(\tau_n\), \(n=1,2,3\), have at most twoelements. If \(x\in A\) has a \(\varrho\)-representative \(u\in D\) andthere is an \(n=1,2,3\) such that \(u\in D_n\), then choose the smallest \(n\)with this property and define \(f(x)=u\), where \(\{u,f(x)\}\in D_n\).Armbrust [1986].
Howard-Rubin number: 1 CY
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