6
votes
2answers
526 views

Is there one binary operation foundational for set theory?

The membership relationship "$\epsilon$" is foundational for set theory, in the sense that the axioms of any set theory are formulated in the language of "$\epsilon$". Naturally, the question arises ...
4
votes
1answer
143 views

If questions are formalized as ideals of a boolean algebra, what kind of algebra of questions appears from Stone representation theorem?

Affirmative propositions make up a Boolean algebra, and Boolean algebras became part of classical algebra for over one century ago - in this sense they are "simple". But I did not encounter in ...
-1
votes
1answer
153 views

Algebra generated by a tree [Edit] [closed]

Suppose that $(T,\leq)$ is a partially ordered set, we say $T$ is a tree* if for every $i\in T$, $\{s: s\in T, s\leq t\}$ is a well-founded chain. What I need to know is: Can the algebra ...
10
votes
1answer
314 views

Formally undecidable problems on finitely presented quandles

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 ...
14
votes
1answer
781 views

Is Dependent Choice equivalent to the statement that every PID is factorial?

In this question, it was asked if AC is needed in the proof of the well-known fact that every principal ideal domain is factorial. As KConrad and Joel David Hamkins have pointed out, only DC, the ...
4
votes
1answer
339 views

Mechanically instantiating abstract constructions

I am looking for work on the effective inverse of abstraction, aka specialization. There are two ways in which abstraction helps us: Get a better understanding of the structural rules at play in ...
3
votes
2answers
761 views

computation, algebra, logic

So a really simple way of describing a digital computer is to say that it is a device for performing boolean operations. You feed it a bunch of bit strings, which is a description of the problem and ...