# Questions tagged [decidability]

Use this tag for questions about the existence of an algorithm that can and will return a correct true or false value to a decision problem.

96 questions
64 views

### Model Theoretical Interpretation of the Incompleteness of Number Theory

This question was sparked by this Numberphile video: https://www.youtube.com/watch?v=O4ndIDcDSGc. Near the end, (12:05), he speaks about the Riemann Hypothesis. He describes that if Riemann is shown ...
31 views

### Do game theoretic issues make the Monty Hall problem undecidable?

If we consider the Monty Hall problem de novo, it is evident that much depends on the strategy of the host. The wiki article on the problem lists possible host strategies. For example, there is Monty ...
32 views

### Why can't the sequent calculus for First-Order Classical Logic be used for proving decidability via Proof-search?

I understand that Turing reduced the halting problem to the satisfiability problem of first-order logic thus proving first-order logic undecidable. However, when thinking about the sequent calculus ...
47 views

### Difference of two decidable languages?

I've been learning about TMs in class lately and we talked about the decidability of two languages by union or intersection. I was wondering if you have two decidable languages, L1 and L2, is their ...
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### Weakened versions of Word and Isomorphism Problems in group theory

Here are my questions: (Weakened Word Problem) Let $\langle X |R\rangle$ be a finite presentation of a group $G$, and let $w$ be an element of the free group $F(X)$. Does there exist an algorithm (...
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### Can we enumerate finite sequences which have no halting continuation?

Note: this is a cross-post from CS.SE, since I haven't gotten an answer there. I am trying to deepen my understanding of the relationship between the Halting Problem and Godel's Completeness Theorem (...
28 views

### Symbols of the language vs. Free variables

For some context: I'm currently taking a course of Formal Methods and Logics and there's a passage where we show that the monadic second order ($\text{MSO}$) theory of (possibly labelled) linear ...
12 views