Related papers: Polish G-spaces, the generalized model theory and …
Given Polish space $\mathcal{Y}$ and a continuous language $L$ we study the corresponding logic $\mathsf{Iso}(\mathcal{Y})$-space $\mathcal{Y}_L$. We build a framework of generalized model theory towards analysis of Borel complexity of…
We analyse logic actions of Polish groups which arise in continuous logic. We extend the generalised model theory of H.Becker to the case of Polish G-spaces when G is an arbitrary Polish group.
In this paper we further develop the theory of canonical approximations of Polishable subgroups of Polish groups, building on previous work of Solecki and Farah--Solecki. In particular, we obtain a characterization of such canonical…
We study Polish spaces for which a set of possible distances $A \subseteq \mathbb{R}^+$ is fixed in advance. We determine, depending on the properties of $A$, the complexity of the collection of all Polish metric spaces with distances in…
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…
We introduce and study the notion of functorial Borel complexity for Polish groupoids. Such a notion aims at measuring the complexity of classifying the objects of a category in a constructive and functorial way. In the particular case of…
We give, for each level of complexity L, a Hurewicz-like characterization of the Borel subsets with countable sections of a product of two Polish spaces that cannot become in L by changing the two Polish topologies.
We study the complexity with respect to Borel reducibility of the relations of isometry and isometric embeddability between ultrametric Polish spaces for which a set $D$ of possible distances is fixed in advance. These are, respectively, an…
We propose and study a new approach to the topologization of spaces of (possibly not all) future-directed causal curves in a stably causal spacetime. It relies on parametrizing the curves "in accordance" with a chosen time function. Thus…
We present and thoroughly study natural Polish spaces of separable Banach spaces. These spaces are defined as spaces of norms, resp. pseudonorms, on the countable infinite-dimensional rational vector space. We provide an exhaustive…
This paper presents a study of generic elements in full isometry groups of Polish ultrametric spaces. We obtain a complete characterization of Polish ultrametric spaces X whose isometry group Iso(X) contains an open subgroup H with ample…
We study strong types and Galois groups in model theory from a topological and descriptive-set-theoretical point of view, leaning heavily on topological dynamical tools. More precisely, we give an abstract (not model theoretic) treatment of…
If G is a Polish group, then there is a Polish G-space X which is universal among Polish G-spaces with respect to continuous G-embeddings.
We give a partial answer to an important open problem in descriptive set theory, the Decomposability Conjecture for Borel functions on an analytic subset of a Polish space to a separable metrizable space. Our techniques employ deep results…
A topological space is almost locally compact if it contains a dense locally compact subspace. We generalize a result from \cite{Ma}, showing that isomorphism on Borel classes of almost locally compact Polish metric structures is always…
We study the complexity of the isomorphism relation for various classes of closed subgroups of the group of permutations of the natural numbers. We use the setting of Borel reducibility between equivalence relations on Polish spaces. For…
The development of the Bielik v3 PL series, encompassing both the 7B and 11B parameter variants, represents a significant milestone in the field of language-specific large language model (LLM) optimization. While general-purpose models…
We introduce a family of modal expansions of {\L}ukasiewicz logic that are designed to accommodate modal translations of generalized basic logic (as formulated with exchange, weakening, and falsum). We further exhibit algebraic semantics…
It is common knowledge in the set theory community that there exists a duality relating the commutative $C^*$-algebras with the family of $B$-names for complex numbers in a boolean valued model for set theory $V^B$. Several aspects of this…
This study investigates the relationship between the phonological and morphological structure of Polish words and their meanings using Distributional Semantics. In the present analysis, we ask whether there is a relationship between the…