Zobrazeno 1 - 10
of 1 384
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
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
Autor:
Montalbán, Antonio, Rossegger, Dino
We calculate the possible Scott ranks of countable models of Peano arithmetic. We show that no non-standard model can have Scott rank less than $\omega$ and that non-standard models of true arithmetic must have Scott rank greater than $\omega$. Other
Externí odkaz:
http://arxiv.org/abs/2208.01697