Zobrazeno 1 - 10
of 3 342
pro vyhledávání: '"Rossegger, A"'
We show that if $E$ is a countable Borel equivalence relation on $\mathbb{R}^n$, then there is a closed subset $A \subset [0,1]^n$ of Hausdorff dimension $n$ so that $E \restriction A$ is smooth. More generally, if $\leq_Q$ is a locally countable Bor
Externí odkaz:
http://arxiv.org/abs/2410.22034
Feferman proved in 1962 that any arithmetical theorem is a consequence of a suitable transfinite iteration of full uniform reflection of $\mathsf{PA}$. This result is commonly known as Feferman's completeness theorem. The purpose of this paper is two
Externí odkaz:
http://arxiv.org/abs/2405.09275
Autor:
Ho, Meng-Che "Turbo", Le, Khanh, Rossegger, Dino
We answer a question of Calderoni and Clay by showing that the conjugation equivalence relation of left orderings of the Baumslag-Solitar groups $\mathrm{BS}(1,n)$ is hyperfinite for any $n$. Our proof relies on a classification of $\mathrm{BS}(1,n)$
Externí odkaz:
http://arxiv.org/abs/2405.08442
We investigate natural variations of behaviourally correct learning and explanatory learning -- two learning paradigms studied in algorithmic learning theory -- that allow us to ``learn'' equivalence relations on Polish spaces. We give a characteriza
Externí odkaz:
http://arxiv.org/abs/2403.17493
We investigate the descriptive complexity of the set of models of first-order theories. Using classical results of Knight and Solovay, we give a sharp condition for complete theories to have a $\boldsymbol\Pi_\omega^0$-complete set of models. We also
Externí odkaz:
http://arxiv.org/abs/2402.10029
We adapt the classical notion of learning from text to computable structure theory. Our main result is a model-theoretic characterization of the learnability from text for classes of structures. We show that a family of structures is learnable from t
Externí odkaz:
http://arxiv.org/abs/2402.05744
Autor:
Gonzalez, David, Rossegger, Dino
We study possible Scott sentence complexities of linear orderings using two approaches. First, we investigate the effect of the Friedman-Stanley embedding on Scott sentence complexity and show that it only preserves $\Pi^{\mathrm{in}}_{\alpha}$ compl
Externí odkaz:
http://arxiv.org/abs/2305.07126
Autor:
Bazhenov, Nikolay, Fokina, Ekaterina, Rossegger, Dino, Soskova, Alexandra A., Vatev, Stefan V.
We prove an effective version of the Lopez-Escobar theorem for continuous domains. Let $Mod(\tau)$ be the set of countable structures with universe $\omega$ in vocabulary $\tau$ topologized by the Scott topology. We show that an invariant set $X \sub
Externí odkaz:
http://arxiv.org/abs/2301.09940
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
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