All Questions
Tagged with universal-algebra algebraic-systems
9 questions
3
votes
0
answers
91
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Algebraic logical structure
Let $M=(W,R)$ be a Kripke frame, $A=(f_1,...,f_m)$ is a tuple of operations $f_i:W^{n_i}\to W$, and $\Phi=(\varphi_1,...,\varphi_m )$ is a tuple of first-order logic formulas in vocabulary $\sigma=\{=...
- 107
2
votes
0
answers
109
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Function and algebraic system
Let $f$ be a surjective function from $X$ to $\{1,2,3\}$. Let $* :X^2 \to X$, such that $$f(x)\neq f(y) \implies f(x) \neq f(xy)\neq f(y), $$ and $$f(x)=f(y)\implies f(x)=f(xy).$$ Let's call the ...
- 107
11
votes
1
answer
462
views
Invariant theory in universal algebra
Let $\mathcal{L}$ be a finite first-order language with no relation symbols and let $\mathcal{K}:=\mathcal{V}(\Theta)$ be a variety in this language defined by a set of identities $\Theta$.
My ...
- 3,318
4
votes
1
answer
214
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The question about elementary equivalence of free products
Let $A,B,C,D$ be algebraic systems and $A$ and $B$ be elementary equivalent as well as $C$ and $D$. Are free products of $A,C$ and $B,D$ elementary equivalent if
$A,B,C,D$ are groups, or
$A,B,C,D$ ...
- 41
5
votes
0
answers
188
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Algebraic/relational structures produced using evolutionary/machine learning algorithms?
Are there examples of algebraic structures which have been constructed using evolutionary algorithms and possibly machine learning algorithms? I am looking for algebraic structures like lattices ...
5
votes
1
answer
245
views
What are algebraic systems and algebraic closure as defined by Kenjiro Shoda? Which are his main results on them?
In On Utumi's ring of quotients, Canad. J. Math. 15(1963), 363-370, J. Lambek says:
As a matter of historical record, the minimal injective extension of a module is a special case of the "algebraic ...
- 2,992
7
votes
0
answers
401
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Universal anti-Horn classes?
Is there published work about universal anti-Horn classes?
Anti-Horn formulas are also sometimes known as dual Horn.
See also related question Is there any research of universal algebras axiomatized ...
- 2,350
6
votes
1
answer
676
views
Generalizations of Birkhoff's HSP Theorem
Let $\mathbf{C}$ be the class of algebraic structures of some fixed type satisfying some sentence $\phi$. Birkhoff's HSP theorem says that $\mathbf{C}$ is closed under homomorphisms, subalgebras and ...
- 1,307
5
votes
2
answers
974
views
Shape of axioms in algebraic structures
When defining algebraic structures (like monoids, groups, etc...), are there some constraints on the shape of the axioms, for the structure to have good properties that we implicitly use in many ...
- 1,341