In the literature, one sometimes sees the claim that finitely presented quandles (in particular, knot quandles) are "hard to deal with". Hence, a great deal of effort has gone into studying finite quandles and counting homomorphisms onto them, and so on. However, I have not yet come across any theorems that state formal undecidability results for finitely presented quandles similar to those for finitely presented groups. In fact, I have yet to see any formulation of such problems. (For instance, a theorem stating that the isomorphism problem is undecidable for finitely presented quandles.)


Do such results exist in the literature and, if so, could someone please provide references?


(Asked previously [here](https://math.stackexchange.com/questions/59285/formally-undecidable-problems-on-finitely-presented-quandles) on math.stackexchange, without response.)



Formally undecidable problems on finitely presented quandles
The word problem for quandles was formulated by Rena Levitt and Sam Nelson. In Levitt's [research statement](http://pages.pomona.edu/~rml04747/Rena_Levitt/Research_files/RLevittResearchStatement.pdf) the problem was formulated as follows: 



> 
> **Word Problem for Quandles.** Given a finitely generated quandle $Q$, is
>  there an algorithm to determine if two words in the generators
>  represent the same element of $Q$?
> 
> 
> 


Levitt and Nelson solved the word problem for some families of quandles. In particular, they proved:



> 
> **Theorem.** Finitely generated free quandles and knot quandles have a
>  solvable word problem.
> 
> 
> 


You can see more information in [these slides](http://pages.pomona.edu/~rml04747/Rena_Levitt/Slides_files/CTopSp2012.pdf) of a talk given by Levitt in 2012. As far as I know, the paper is not yet published. 


