Intereting Posts

Two finite abelian groups with the same number of elements of any order are isomorphic
What is the supremum and infimum of $n/(1+n^2)$ where $n$ is an element of $\mathbb{N}$?
Cohomology of projective plane
How far can one get in analysis without leaving $\mathbb{Q}$?
What is the precise definition of $i$?
Prove a set is not recursive / recursively enumerable
If $A^2$ and $B^2$ are similar matrices, do $A$ and $B$ have to be similar?
Use Gröbner bases to count the $3$-edge colorings of planar cubic graphs…
$p$ divides $n^p-n$
Given a matrix with non-negative real entries, can you algebraically prove that it has a non-negative eigenvalue?
Integral help here please?
arrangement of the word $“\bf{MATHEMATICS}”$ in which no two same letter occur together.
How to estimate the growth of a “savage” function near 1?
big and small O notation help
Integral $\int_0^1 dx \frac{\ln x \ln^2(1-x)\ln(1+x)}{x}$

Several questions on MSE in recent months and most recently this one have made me feel that recursion theory is suffering from terminology bloat. Why have so many synonyms for “recursive” and “recursively enumerable” been introduced?

I can just about see why people might want to use “computable” for recursive or use “computably enumerable”, “Turing-acceptable” or “Turing-recognizable” for recursively enumerable.

I can’t understand why anyone would want to use “decidable” for recursive, “partially decidable” or “semidecidable” for r.e. unless they were talking about sets that are interpreted as logical judgments (like the word problem for group theory) rather than any other sets (like codes of Turing machines). So I think “decidable’ should be reserved for instances of some kind of Entscheidungsproblem.

- When does L' Hopital's rule fail?
- Where to go after calculus?
- Books to study for Math GRE, self-study, have some time.
- The use for solving quadradic equations for high school students
- Books that develop interest & critical thinking among high school students
- Quotient geometries known in popular culture, such as “flat torus = Asteroids video game”

I can just about see how someone could argue that “recognizable” intuitively suggests r.e. but not recursive. But I can’t really see any advantage in changing to use that terminology.

What is going on with the terminology of recursion theory?

- Is metric (Cauchy) completeness “outside the realm” of first order logic?
- Is there a simple group of any (infinite) size?
- An example for a calculation where imaginary numbers are used but don't occur in the question or the solution.
- How to prove that a set of logical connectives is functionally complete(incomplete)?
- Can anyone help me with a solution?
- Consistency of Peano axioms (Hilbert's second problem)?
- Can someone provide the formal definition of the tangent line to a curve?
- “Negative” versus “Minus”
- Do expressions like $(-1)^{2/3}$ show up naturally in pure or applied math?
- Quantifier Notation

- The kernel of the transpose of the differentiation operator – Solution check
- $\operatorname{tr}(AABABB) = \operatorname{tr}(AABBAB)$ for $2×2$ matrices
- Elementary geometry from a higher perspective
- Must a monotone function have a monotone derivative?
- Norm of an inverse operator: $\|T^{-1}\|=\|T\|^{-1}$?
- Closed form for $\int_0^e\mathrm{Li}_2(\ln{x})\,dx$?
- For each $x,y,z∈\mathbb N$, if $x<y$ then $x+z<y+z$
- Proof on p. $16 \;$ of Lang's Algebraic Number Theory
- Finding the kernel of a linear map
- Mathematical symbol for “and”
- Inequality regarding norms and weak-star convergence
- Best fitting in a curve of the form $Ax^B+C$
- $f(x)=\int_{0}^{+\infty} e^{-(t+\frac{1}{t})x}dt$ how to find $f(x)$?
- Rotation by Householder matrices
- Conjugacy classes in $A_n$.