Recent zbMATH articles in MSC 08Bhttps://zbmath.org/atom/cc/08B2022-07-25T18:03:43.254055ZUnknown authorWerkzeugHomogeneous structures: model theory meets universal algebra. Abstracts from the workshop held January 3--9, 2021 (online meeting)https://zbmath.org/1487.000322022-07-25T18:03:43.254055ZSummary: The workshop ``Homogeneous Structures: Model Theory meets Universal Algebra'' was centred around transferring recently obtained advances in universal algebra from the finite to the infinite. As it turns out, the notion of homogeneity together with other model-theoretic concepts like \(\omega\)-categoricity and the Ramsey property play an indispensable role in this endeavour.Maltsev conditions for general congruence meet-semidistributive algebrashttps://zbmath.org/1487.080022022-07-25T18:03:43.254055Z"Olšák, Miroslav"https://zbmath.org/authors/?q=ai:olsak.miroslavAuthor's abstract: Meet semidistributive varieties are in a sense the last of the most important classes in universal algebra for which it is unknown whether it can be characterized by a strong Maltsev condition. We present a new, relatively simple Maltsev condition characterizing the meet-semidistributive varieties, and provide a candidate for a strong Maltsev condition.
Reviewer: Agata Pilitowska (Warszawa)Structure of quasivariety lattices. IV: Nonstandard quasivarietieshttps://zbmath.org/1487.080032022-07-25T18:03:43.254055Z"Kravchenko, A. V."https://zbmath.org/authors/?q=ai:kravchenko.alexandr-v"Nurakunov, A. M."https://zbmath.org/authors/?q=ai:nurakunov.anvar-m"Schwidefsky, M. V."https://zbmath.org/authors/?q=ai:schwidefsky.marinaLet \(\sigma\) be a finite signature and let \(\mathcal M\) be a quasivariety of signature \(\sigma\). According to Definition 4 of the paper, a class \(\mathcal A=\{\mathbb A_X\;|\;X\in {\mathcal P}_{\textrm{fin}}(\omega)\}\subseteq {\mathcal M}\) of finite \(\sigma\)-structures is called a \textit{finite \(B\)-class} with respect to \(\mathcal M\) if
\begin{itemize}
\item[(\(B_0\))] \(\mathbb A_{\emptyset}\) is a trivial structure.
\item[(\(B_1\))] if \(X = Y \cup Z\) in \({\mathcal P}_{\textrm{fin}}(\omega)\), then \(\mathbb A_X\) belongs to the quasivariety generated by \(\mathbb A_Y\) and \(\mathbb A_Z\).
\item[(\(B_2\))] if \(\emptyset\neq X\in {\mathcal P}_{\textrm{fin}}(\omega)\) and \(\mathbb A_X\) belongs to the quasivariety generated by \(\mathbb A_Y\), then \(X=Y\).
\item[(\(B_3\))] if \(F \in {\mathcal P}_{\textrm{fin}}(\omega)\), \(i \in \omega\), and \(f \in \textrm{Hom}(\mathcal A_F, A_{\{i\}})\), then either \(f(\mathbb A_F) \cong \mathbb A_{\emptyset}\) or \(i \in F\).
\item[(\(B_4\))] if \(F \in {\mathcal P}_{\textrm{fin}}(\omega)\), then any homomorphic image of \(\mathbb A_F\) that lies in \(\mathcal M\) must lie in \(\mathcal A\).
\end{itemize}
The main results of the paper are that if \(\mathcal M\) is a quasivariety with a finite \(B\)-class, then \(\mathcal M\) has continuously many nonstandard subquasivarieties, each of which has a finitely partitionable independent quasiequational basis relative to \(\mathcal M\) (Theorem 5), and \(\mathcal M\) has continuously many nonstandard subquasivarieties, none of which has a finitely partitionable independent quasiequational basis relative to \(\mathcal M\) (Theorem 4). The paper concludes with a section that provides many examples of quasivarieties containing a finite \(B\)-class.
For Part III see [the authors, Algebra Logic 59, No. 3, 222--229 (2020; Zbl 1484.08016); translation from Algebra Logika 59, No. 3, 323--333 (2020)].
Reviewer: Keith Kearnes (Boulder)Non-relativistic limits of general relativityhttps://zbmath.org/1487.831432022-07-25T18:03:43.254055Z"Bergshoeff, Eric"https://zbmath.org/authors/?q=ai:bergshoeff.eric-a"Lahnsteiner, Johannes"https://zbmath.org/authors/?q=ai:lahnsteiner.johannes"Romano, Luca"https://zbmath.org/authors/?q=ai:romano.luca"Rosseel, Jan"https://zbmath.org/authors/?q=ai:rosseel.jan"Şimşek, Ceyda"https://zbmath.org/authors/?q=ai:simsek.ceydaSummary: We discuss non-relativistic limits of general relativity. In particular, we define a special fine-tuned non-relativistic limit, inspired by string theory, where the Einstein-Hilbert action has been supplemented by the kinetic term of a one-form gauge field. Taking the limit, a crucial cancellation takes place, in an expansion of the action in terms of powers of the velocity of light, between a leading divergence coming from the spin-connection squared term and another infinity that originates from the kinetic term of the one-form gauge field such that the finite invariant non-relativistic gravity action is given by the next subleading term. This non-relativistic action allows an underlying torsional Newton-Cartan geometry as opposed to the zero torsion Newton-Cartan geometry that follows from a more standard limit of General Relativity but it lacks the Poisson equation for the Newton potential. We will mention extensions of the model to include this Poisson equation.
For the entire collection see [Zbl 1482.94007].