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Let me mention as a counterpoint that there is less need for new terminology than one might expect. … Mathematical exposition is often more successful and clearer without new terminology, and one should consider whether one needs any new terminology at all. …

To my way of thinking, the other answers are missing an important element, a necessary feature for a mathematical tool or method to be called "trick." Namely, in order to be called a "trick," a metho …

recasting of entire schemes of terminology to focus on what was all along the actual focus, namely, the concept of computability, rather than specifically recursion. … This text was called, "Recursively enumerable sets and degrees," using the old terminology, but Soare preferred to recast it as "Computably enumerable sets and degrees." …

Your question amounts to treating construction problems in geometry as decision problems, and so it makes sense to me to adopt the terminology of computability theory. … This same kind of distinction arises in computability theory, where we have the following terminology: A set $A$ is decidable if we can computably verify yes-or-no whether a given input $a$ is in $A$ …

Define an order on pairs of ordinals $(\alpha,\beta)$ by ordering first by maximum, then by first coordinate, then by second coordinate. That is, one pair preceeds another if the maximum is smaller, o …

The term "class" is not a technical term with a universally definite meaning, but there are various established meanings in various contexts. In ZFC the established usage as Wojowu mentions in the com …

In spaces where singleton points are closed, your property is equivalent to saying that the space has no isolated points. Or in other words, that it is perfect. Clearly, no space with an isolated po …

In that terminology, trees of your first kind are known as the well-founded trees, since they are trees where the tree order is well-founded (and well-founded linear orders are the same as well-orders) … I think that the situation is that because set theorists are mainly interested in the well-founded case, the terminology evolved to drop the adjective from well-founded trees. …

The subscript $0$ is meant to indicate the amount of induction that the theory has. The wikipedia entry on Reverse mathematics says of the big five theories of reverse mathematics that The …

Here is one way to view the so-called ordering principle as a selection principle. Theorem. The following are equivalent over ZF set theory: Every set admits a linear order. For every set $X$, there …

The answer is no for uncountable cardinals $\kappa$. Let $\mathfrak{A}=\langle A,U\rangle$ be a set $A$ of size $\kappa$ with a unary predicate $U\subset A$, where $U$ and $A-U$ both have size $\kappa …

Injective and functional are completely standard in this case. This is what you should use. The term "functional" is not overloaded, when you are using it to say that something is a function. Being fu …

Therefore, unlesss there is already an established terminology for your ordinals coming from fine-structure theory (see below), I would suggest the terminology: $\alpha$ is sententially categorical with … I am not sure if they isolate your notion exactly with terminology, but that is where I would look. …

I like your concept a lot, and have been able to find a characterization. Suppose that $f:N\to N$ is effectively closed in your sense. First, as you mentioned, it is easy to see that $\text{ran}(f)$ …

A partial order with no infinite descending chains is said to be well-founded. Every well-founded partial order admits an ordinal ranking function, an assignment of nodes in the order to ordinals, suc …