Sentence examples for a membership relation from inspiring English sources

Fig. 5 a Membership relation between models and descriptors.

This does not dictate that proteins and genetic products are one and the same, but rather allows the expression of a membership relation at a much finer semantic resolution such that proteins can be understood as one, but not the sole, kind of gene product (which also includes RNA).

for which ƒi = h ○ σi for all i ∈ I. 4. I.e., such that no contradictions can be derived from Δ using the deductive machinery in P. 5. If A is a set, ∈ ⨡ A denotes the membership relation on A, i.e., {⟨x, y⟩ ∈ A × A : x ∈ y}. 6. Strictly speaking, this is only the case when κ is regular, that is, not the limit of < κ cardinals each of which is < κ.

We now define a new membership relation E so that xEy iff either the second component of k y) is 1 and x ∈ first component, or the second component of k y) is 0 and x ∉ first component.

We reserve judgement on this — we do note that the theorem "the ordinals in any (set!) model of NFU are not well-ordered" is a theorem of NFU itself; note that NFU does not see the universe as a model of NFU (even though it is a set) because the membership relation is not a set relation (if it were, the singleton map certainly would be).

Any model which gets membership right will have to have a well-founded membership relation.

It should be noted that this is not merely a logically necessary property of equality but an assumption about the membership relation as well.

The definite relation that may or may not exist between an object and a set is called the membership relation.

Then f is an isomorphism from M to a structure whose universe is the disjoint union of a set A and its power set P(A) and which assigns A to I, assigns P(A) to S, and assigns the membership relation ∈ to E.   So roughly speaking, σ defines the power-set operation "to within isomorphism".

Then to express the idea that S is the power set of I we can use the conjunction (call it σ) of the following four sentences: Clearly σ is true in any structure whose universe is the disjoint union of a set A and its power set P(A) and which assigns A to I, assigns P(A) to S, and assigns the membership relation ∈ to E.   Conversely, let M be any model of σ (in the standard semantics).

This is a descending sequence in the membership relation, something forbidden by FA.