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pro vyhledávání: '"CSIMA, BARBARA F."'
Given a reduced abelian $p$-group, we give an upper bound on the Scott complexity of the group in terms of its Ulm invariants. For limit ordinals, we show that this upper bound is tight. This gives an explicit sequence of such groups with arbitrarily
Externí odkaz:
http://arxiv.org/abs/2407.06940
Walker's Cancellation theorem for abelian groups tells us that if $A$ is finitely generated and $G$ and $H$ are such that $A \oplus G \cong A \oplus H$, then $G \cong H$. Michael Deveau showed that the theorem can be effectivized, but not uniformly.
Externí odkaz:
http://arxiv.org/abs/2309.01844
Autor:
Csima, Barbara F., Rossegger, Dino
We give a characterization of the strong degrees of categoricity of computable structures greater or equal to $\mathbf 0''$. They are precisely the \emph{treeable} degrees -- the least degrees of paths through computable trees -- that compute $\mathb
Externí odkaz:
http://arxiv.org/abs/2209.04524
We study countable structures from the viewpoint of enumeration reducibility. Since enumeration reducibility is based on only positive information, in this setting it is natural to consider structures given by their positive atomic diagram -- the com
Externí odkaz:
http://arxiv.org/abs/2206.01135
Publikováno v:
The Bulletin of Symbolic Logic, 2023 Mar 01. 29(1), 1-18.
Externí odkaz:
https://www.jstor.org/stable/27201652
Akademický článek
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When classes of structures are not first-order definable, we might still try to find a nice description. There are two common ways for doing this. One is to expand the language, leading to notions of pseudo-elementary classes, and the other is to all
Externí odkaz:
http://arxiv.org/abs/1808.01588
The rate of randomness (or dimension) of a string $\sigma$ is the ratio $C(\sigma)/|\sigma|$ where $C(\sigma)$ is the Kolmogorov complexity of $\sigma$. While it is known that a single computable transformation cannot increase the rate of randomness
Externí odkaz:
http://arxiv.org/abs/1806.05936
A computable structure $\mathcal{A}$ has degree of categoricity $\mathbf{d}$ if $\mathbf{d}$ is exactly the degree of difficulty of computing isomorphisms between isomorphic computable copies of $\mathcal{A}$. Fokina, Kalimullin, and Miller showed th
Externí odkaz:
http://arxiv.org/abs/1805.10249
Autor:
Csima, Barbara F., Dzhafarov, Damir D., Hirschfeldt, Denis R., Jockusch, Jr., Carl G., Solomon, Reed, Westrick, Linda Brown
Hindman's Theorem (HT) states that for every coloring of $\mathbb N$ with finitely many colors, there is an infinite set $H \subseteq \mathbb N$ such that all nonempty sums of distinct elements of $H$ have the same color. The investigation of restric
Externí odkaz:
http://arxiv.org/abs/1804.09809