7 research outputs found
Dominions and Primitive Positive Functions
Let A C such that g and g´ agree on A, we have g = g´. Our main theorem states that if K is closed under ultraproducts, then A dominates b relative to K if and only if there is a partial function F definable by a primitive positive formula in K such that F(a1 ,...,an) = b for some a1,...,an in A. Applying this result we show that a quasivariety of algebras Q with an n-ary near-unanimity term has surjective epimorphisms if and only if SPPu(Q_RSI) has surjective epimorphisms. It follows that if F is a finite set of finite algebras with a common near-unanimity term, then it is decidable whether the (quasi)variety generated by F has surjective epimorphisms.Fil: Campercholi, Miguel Alejandro Carlos. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentin
Epimorphisms, definability and cardinalities
We characterize, in syntactic terms, the ranges of epimorphisms in an arbitrary class of similar first-order structures (as opposed to an elementary class). This allows us to strengthen a result of Bacsich, as follows: in any prevariety having at most s non-logical symbols and an axiomatization requiring at most m variables, if the epimorphisms into structures with at most m+s+ℵ0 elements are surjective, then so are all of the epimorphisms. Using these facts, we formulate and prove manageable ‘bridge theorems’, matching the surjectivity of all epimorphisms in the algebraic counterpart of a logic ⊢ with suitable infinitary definability properties of ⊢, while not making the standard but awkward assumption that ⊢ comes furnished with a proper class of variables.The European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 689176 (project “Syntax Meets Semantics: Methods, Interactions, and Connections in Substructural logics”). The first author was also supported by the Project GA17-04630S of the Czech Science Foundation (GAČR). The second author was supported in part by the National Research Foundation of South Africa (UID 85407). The third author was supported by the DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa.http://link.springer.com/journal/112252020-02-07hj2019Mathematics and Applied Mathematic
Epimorphism Surjectivity in Logic and Algebra
Treballs Finals del Màster de Lògica Pura i Aplicada, Facultat de Filosofia, Universitat de Barcelona. Curs: 2023-2024. Tutor: Luca Carai and Tommaso MoraschiniAs the theorems we aim to prove require a variety of tools and background theory,
we will start by recalling some basics of first-order logic (Section 2.1), model theory
(Section 2.2), and universal algebra (Section 2.3). We will then continue presenting
the protagonist of this thesis, the epimorphism surjectivity property, and making
some easy but useful observations concerning this property (Section 2.4). Finally, we
will establish a correspondence between the (weak) ES property in algebra and the
(finite) Beth definability property in logic, providing motivation for the study of the
ES property from a logical standpoint (Section 2.5
Epimorphisms in varieties of subidempotent residuated structures
A commutative residuated lattice A is said to be subidempotent if the lower
bounds of its neutral element e are idempotent (in which case they naturally
constitute a Brouwerian algebra A*). It is proved here that epimorphisms are
surjective in a variety K of such algebras A (with or without involution),
provided that each finitely subdirectly irreducible algebra B in K has two
properties: (1) B is generated by lower bounds of e, and (2) the poset of prime
filters of B* has finite depth. Neither (1) nor (2) may be dropped. The proof
adapts to the presence of bounds. The result generalizes some recent findings
of G. Bezhanishvili and the first two authors concerning epimorphisms in
varieties of Brouwerian algebras, Heyting algebras and Sugihara monoids, but
its scope also encompasses a range of interesting varieties of De Morgan
monoids
Idempotent residuated structures : some category equivalences and their applications
This paper concerns residuated lattice-ordered idempotent commutative
monoids that are subdirect products of chains. An algebra of this
kind is a generalized Sugihara monoid (GSM) if it is generated by the lower
bounds of the monoid identity; it is a Sugihara monoid if it has a compatible
involution :. Our main theorem establishes a category equivalence
between GSMs and relative Stone algebras with a nucleus (i.e., a closure
operator preserving the lattice operations). An analogous result is obtained
for Sugihara monoids. Among other applications, it is shown that Sugihara
monoids are strongly amalgamable, and that the relevance logic RMt has
the projective Beth de nability property for deduction.http://www.ams.org//journals/tran/hb201
Semilinear De Morgan monoids and epimorphisms
DATA AVAILABILITY : Data sharing not applicable to this article as datasets were neither generated nor analysed.A representation theorem is proved for De Morgan monoids that are (i) semilinear, i.e., subdirect products of totally ordered algebras, and (ii) negatively generated, i.e., generated by lower bounds of the neutral element. Using this theorem, we prove that the De Morgan monoids satisfying (i) and (ii) form a variety—in fact, a locally finite variety. We then prove that epimorphisms are surjective in every variety of negatively generated semilinear De Morgan monoids. In the process, epimorphism-surjectivity is established for several other classes as well, including the variety of all semilinear idempotent commutative residuated lattices and all varieties of negatively generated semilinear Dunn monoids. The results settle natural questions about Beth-style definability for a range of substructural logics.The Operational Programme Research,
Development and Education of the Ministry of Education, Youth and Sports of the Czech
Republic, the EU and in part by the
National Research Foundation of South Africa. Open access funding provided by University of Pretoria.https://link.springer.com/journal/12hj2024Mathematics and Applied MathematicsNon
Материалы конференции: "Алгебра и математическая логика: теория и приложения"
Сборник содержит тезисы докладов, представленных на международную конференцию "Алгебра и математическая логика: теория и приложения" ( г. Казань 2-6 июня 2014 год) и сопутствующую молодежную летнюю школу "Вычислимость и вычислимые структуры", посвященную 210-летию Казанского университета, 80-летию со дня основания кафедры алгебры (ныне кафедры алгебры и математической логики) Казанского университета Н.Г. Чеботаревым и 70-летию со дня рождения зав. кафедрой члена-корреспондента АН РТ М.М. Арсланова.17