All Questions
9 questions
13
votes
2
answers
1k
views
What's the deal with De Morgan algebras and Kleene algebras?
The notion of Boolean algebras, and the corresponding classical propositional logic, is very standard, and it is easy to find information about them (for example, among many other such works, there is ...
- 32.5k
6
votes
0
answers
179
views
Elementary equivalence for rings
Let $\mathcal{L}$ be a first-order language, and $M$ and $N$ be two $\mathcal{L}$-structures. We say that $M$ and $N$ are elementarily equivalent (write $M \approx N$) if they satisfy the same first-...
- 3,318
12
votes
0
answers
542
views
Does Wedderburn's Little Theorem hold constructively?
Wedderburn's Little Theorem states that every finite division ring is commutative. Perhaps even more surprising, this implies that every finite reduced ring is commutative.
The proofs that I am aware ...
- 63.1k
5
votes
0
answers
302
views
Reference for countable and uncountable algebraic closures of $\mathbb{Q}$ in ZF
The following facts seem to be part of the folklore (where $\mathsf{ZF}$ means Zermelo-Fraenkel set theory with no axiom of choice):
it is consistent with $\mathsf{ZF}$ that there exists an ...
- 32.5k
1
vote
2
answers
157
views
Link btw. exponential and derivatives from an algebraic perspective [closed]
I have been attempting to understand my math education (as a bachelor in electrical engineering) from a more algebraic perspective recently. I would like to understand more about the link between ...
-1
votes
1
answer
417
views
Conversion of logic formula into algebraic formula
We know formula of boolean algebra in canonical disjunctive normal form has or may be converted to Zhegalkin polynomial.
Is there any approach to convert first order formula into algebraic function ...
- 3,094
20
votes
3
answers
2k
views
How do I apply the Boolean Prime Ideal Theorem?
I have become aware of an amazing phenomenon from a myriad of questions and answers here on MathOverflow: many of the results that I would typically prove using the Axiom of Choice can actually be ...
- 5,407
1
vote
1
answer
272
views
Self-similarity for simple algebraic structures [closed]
I'm doing this thread because I have some ideas about how to define self-similarity in algebra, but I don't know if this is known at all. Any critics, comments and references are more than welcomed. ...
- 438
15
votes
1
answer
1k
views
Are wild problems related to undecidable ones?
In representation theory, there is a well-known notion of a wild classification problem (such problems have been discussed often on this forum, for example, here). In logic, there is a notion of an ...
- 5,654