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20
votes
0answers
382 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 ...
11
votes
0answers
341 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 ...
4
votes
0answers
156 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
42 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
130 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 ...
2
votes
0answers
104 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
16 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
69 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
82 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
49 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