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21
votes
0answers
421 views

Decidability of equality of elementary expressions

In the following definition the term expression is to be understood as a finite tree built from formal symbols without any predefined meaning assigned to them. Define the set $\mathcal{E}$ of ...
12
votes
0answers
186 views

Is tightness decidable?

Given a contact structure on a three-manifold, is there an algorithm to decide whether or not it tight? For concreteness' sake, let's agree to represent the given contact three-manifold via an open ...
11
votes
0answers
393 views

Decidability of $x^3+y^3+z^3 = c$

I wondering if it is known whether the following problem is algorithmically decidable or undecidable by Turing machines: given an integer c, determine if there are integers $(x,y,z)$ such that $x^3+y^...
7
votes
0answers
231 views

Proving Richardson's theorem for constants

(I asked this a little over 3 months ago on math.SE, and when I initially re-asked here, no one had responded there. $\:$ After I re-asked here, Eric Towers responded there, since I had forgotten to ...
5
votes
0answers
147 views

List of finitely presented groups with undecidable word problem

Is there any reasonably updated list of (representative) examples of finitely presented groups with undecidable word problem? By "representative" I mean "avoiding obvious redundancy", i.e. examples ...
4
votes
0answers
216 views

Is the two variable fragment of arithmetic, i.e., theory of ($\mathbb{N}, + ,\times$), decidable?

Any references would be appreciated. Most places only address different vocabularies (e.g. a survey of arithmetical definability by Bes).
4
votes
0answers
114 views

Undecidability of the existential theory

Do you know if I can find the proof that the existential theory of $\mathbb{Z}$ with the structure of addition , divisibility and the relation $(\exists s \in \mathbb{Z})m=np^s$ is undecidable, ...
4
votes
0answers
162 views

The theory of two finite linear orders

My colleague Matthias Baaz is looking for a reference for the following question (or possibly theorem): Let T be the "theory of pairs of finite linear orders". That is, consider all finite ...
2
votes
0answers
87 views

Positive existential theory of $(\mathbb{Z}; +, |_n)$

I am reading a paper and there is the following theorem: Let $n$ be a fixed integer, and $n >1$. Denote divisibility in $\mathbb{Z}[\frac{1}{n}]$ by $|_n$, thus for all $x, y \in \...
2
votes
0answers
44 views

Decidability of first order theory of subclasses of posets

Is the first order theory of finite posets known to be undecidable? Does anyone know a survey about such results?
2
votes
0answers
133 views

What is the general feeling for Hilbert's 10th problem for Q?

We know that Hilbert's 10th problem for $\mathbb{Z}$ is undecidable. I was wondering whether there is a strong opinion in the mathematical community on the decidability of Hilbert's 10th for $\mathbb{...
2
votes
0answers
108 views

Extend Lowenheim's decidability result to fragment of second-order logic

Since relational monadic first-order logic has finite model property, its SAT problem is decidable. In H.Behmann's paper, he extended this result to fragment of SOL where all predicates, free and ...
1
vote
0answers
33 views

Relation between indexed languages (OI-macro or context-free tree) and scattered context languages

I'm not sure about the relation between indexed languages (generated by indexed grammars--Aho) and scattered context languages (generated by scattered context grammars--J Hopcroft). I think that ...
1
vote
0answers
74 views

What is the generic complexity of First Order Predicate Calculus?

I suspect that it should be the same as that of the Turing machine halting problem, which wikipedia gives as GenP and attributes this result to Hamkins and Miasnikov, but I am not sure. Is the generic ...
1
vote
0answers
84 views

unique types and decidability

Suppose $\mathcal{M}$ is an infinite structure which has the property that every type that is realised is realised uniquely. Also assume that every element of $\mathcal{M}$ is definable but there is ...
0
votes
0answers
150 views

Is the positive existential theory undecidable?

Could you tell if the positive existential theory of $\mathbb{C}[e^{\mu x} \mid \mu \in \mathbb{C}]$ is undecidable in the language $\{+, \cdot , \frac{d}{dx} , 0, 1, e^x\}$ ? How can we prove the (...
0
votes
0answers
50 views

Is the question whether a FO formula F has a model of size k (k is a finite number) decidable?

Hi all, can someone please tell me whether the question whether a FO formula F has a model of size k (where k is a finite number) is decidable? Thanks in advance! TL