unary predicates
question: What kind of predicates are understood as the divider of the domain of discourse?, context: When there are only finitely many sorts in a theory, many-sorted first-order logic can be reduced to single-sorted first-order logic. One introduces into the single-sorted theory a unary predicate symbol for each sort in the many-sorted theory, and adds an axiom saying that these unary predicates partition the domain of discourse. For example, if there are two sorts, one adds predicate symbols 




P

1


(
x
)


{\displaystyle P_{1}(x)}

 and 




P

2


(
x
)


{\displaystyle P_{2}(x)}

 and the axiom
What kind of predicates are understood as the divider of the domain of discourse?
One introduces into the single-sorted theory a unary predicate symbol for each sort in the many-sorted theory, and adds an axiom saying that these unary predicates partition the domain of discourse.
When there are only finitely many sorts in a theory, many-sorted first-order logic can be reduced to single-sorted first-order logic. One introduces into the single-sorted theory a unary predicate symbol for each sort in the many-sorted theory, and adds an axiom saying that these unary predicates partition the domain of discourse. For example, if there are two sorts, one adds predicate symbols 




P

1


(
x
)


{\displaystyle P_{1}(x)}

 and 




P

2


(
x
)


{\displaystyle P_{2}(x)}

 and the axiom
One introduces into the single-sorted theory a unary predicate symbol for each sort in the many-sorted theory, and adds an axiom saying that these <hl> unary predicates <hl> partition the domain of discourse.
When there are only finitely many sorts in a theory, many-sorted first-order logic can be reduced to single-sorted first-order logic. One introduces into the single-sorted theory a unary predicate symbol for each sort in the many-sorted theory, and adds an axiom saying that these <hl> unary predicates <hl> partition the domain of discourse. For example, if there are two sorts, one adds predicate symbols P 1 ( x ) {\displaystyle P_{1}(x)} and P 2 ( x ) {\displaystyle P_{2}(x)} and the axiom
When there are only finitely many sorts in a theory, many-sorted first-order logic can be reduced to single-sorted first-order logic. <hl> One introduces into the single-sorted theory a unary predicate symbol for each sort in the many-sorted theory, and adds an axiom saying that these unary predicates partition the domain of discourse. <hl> For example, if there are two sorts, one adds predicate symbols P 1 ( x ) {\displaystyle P_{1}(x)} and P 2 ( x ) {\displaystyle P_{2}(x)} and the axiom