11/1/2022 0 Comments Rigid notion definition![]() ![]() In general, an object $X$ of a topos is called decidable (or is said to have a decidable equality) if the diagonal embedding $X \rightarrow X \times X$ is complemented, that is if there exists a sub-object $\Delta^$ to $X$ is relatively hausdorff in the sense that the diagonal embeddings $Y \rightarrow Y \times_X Y$ is a closed embeddings.Īlso this version of "rigidity" is a local property, and stable by arbitrary pullback, whereas I don't think the original definition is. Know precise definitions of angle, circle, perpendicular line, parallel line. There are two more popular routes to define the notion of rigidity for general terms one of them is called here the essentialist approach and the other one the intensionalist approach (it will be discussed in Sections V and VI).7 According to the essentialist approach, a general term is a rigid designator provided it is an essentialist. ![]() Before doing that, we need to define the concept of non-degenerate embedding. Once you have fixed this issue (either by slightly changing your definition, or by restricting yourself to locally connected space) The name your are looking for is "decidable sheaf". We will do this using the notion of interdependent edges in Definition 6. The problem is that your definition is well behaved only if there is enough open subsets $V$ such that $V$ is connected (if there is no such open subset, then your condition is empty) hence the notion as you defined is well behaved only on a locally connected space. Richard Nixon is also rigid by the second definition, which says that a rigid designator refers to the same object in every possible world with respect to which the designator refers. ![]()
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