scholarly journals On Jonsson varieties and quasivarieties

2021 ◽  
Vol 104 (4) ◽  
pp. 151-157
Author(s):  
A.R. Yeshkeyev ◽  
Keyword(s):  
Universal Algebra ◽  
Model Theory ◽  
Positive Answer ◽  
Sufficient Condition ◽  
Basic Concepts ◽  
Locally Convex

In this paper, new objects of research are identified, both from the standpoint of model theory and from the standpoint of universal algebra. Particularly, the Jonsson spectra of the Jonsson varieties and the Jonsson quasivarieties are considered. Basic concepts of 3 types of convexity are given: locally convex theory, ϕ(x)-convex theory, J-ϕ(x)-convex theory. Also, the inner and outer worlds of the model of the class of theories are considered. The main result is connected with the question of W. Forrest, which is related to the existential closed ness of an algebraically closed variety. This article gives a sufficient condition for a positive answer to this question.

scholarly journals On Dentability in Locally Convex Vector Spaces

2017 ◽  
Vol 10 ◽  
pp. 14-19
Author(s):  
Oleg Reinov ◽  
Asfand Fahad
Keyword(s):  
Vector Space ◽  
Wide Class ◽  
Positive Answer ◽  
Vector Spaces ◽  
Bounded Subset ◽  
Locally Convex

The notions of V-dentability, V-s-dentability and V-f-dentability are introduced. It is shown, in particular, that if B is a bounded sequentially complete convex metrizable subset of a locally convex vector space E and V is a neighborhood of zero in E, then the following are equivalent: 1). B is subset V-dentable; 2). B is subset V-s-dentable; 3). B is subset V-f-dentable. It follows from this that for a wide class of locally convex vector spaces E, which strictly contains the class of (BM) spaces (introduced by Elias Saab in 1978), the following is true: every closed bounded subset of E is dentable if and only if every closed bounded subset of E is f-dentable. Also, we get a positive answer to the Saab's question (1978) of whether the subset dentability and the subset s-dentability are the same forthe bounded complete convex metrizable subsets of any l.c.v. space.

scholarly journals Crisp-determinization of weighted tree automata over strong bimonoids

2021 ◽  
Vol vol. 23 no. 1 (Automata, Logic and Semantics) ◽  
Author(s):  
Zoltán Fülöp ◽  
Dávid Kószó ◽  
Heiko Vogler
Keyword(s):  
Finite Order ◽  
Positive Answer ◽  
Order Property ◽  
Sufficient Condition ◽  
Tree Automata ◽  
Weighted Tree ◽  
Bottom Up ◽  
Initial Algebra ◽  
Initial Algebra Semantics ◽  
Weighted Tree Automata

We consider weighted tree automata (wta) over strong bimonoids and their initial algebra semantics and their run semantics. There are wta for which these semantics are different; however, for bottom-up deterministic wta and for wta over semirings, the difference vanishes. A wta is crisp-deterministic if it is bottom-up deterministic and each transition is weighted by one of the unit elements of the strong bimonoid. We prove that the class of weighted tree languages recognized by crisp-deterministic wta is the same as the class of recognizable step mappings. Moreover, we investigate the following two crisp-determinization problems: for a given wta ${\cal A}$, (a) does there exist a crisp-deterministic wta which computes the initial algebra semantics of ${\cal A}$ and (b) does there exist a crisp-deterministic wta which computes the run semantics of ${\cal A}$? We show that the finiteness of the Nerode algebra ${\cal N}({\cal A})$ of ${\cal A}$ implies a positive answer for (a), and that the finite order property of ${\cal A}$ implies a positive answer for (b). We show a sufficient condition which guarantees the finiteness of ${\cal N}({\cal A})$ and a sufficient condition which guarantees the finite order property of ${\cal A}$. Also, we provide an algorithm for the construction of the crisp-deterministic wta according to (a) if ${\cal N}({\cal A})$ is finite, and similarly for (b) if ${\cal A}$ has finite order property. We prove that it is undecidable whether an arbitrary wta ${\cal A}$ is crisp-determinizable. We also prove that both, the finiteness of ${\cal N}({\cal A})$ and the finite order property of ${\cal A}$ are undecidable.

scholarly journals A finite model-theoretical proof of a property of bounded query classes within PH

2004 ◽  
Vol 69 (4) ◽  
pp. 1105-1116 ◽  
Author(s):  
Leszek Aleksander Kołodziejczyk
Keyword(s):  
Normal Form ◽  
Model Theory ◽  
Finite Model ◽  
Sufficient Condition ◽  
Finite Model Theory ◽  
Finite Models ◽  
Constructible Function ◽  
Simple Sufficient Condition

Abstract.We use finite model theory (in particular, the method of FM-truth definitions, introduced in [MM01] and developed in [K04], and a normal form result akin to those of [Ste93] and [G97]) to prove:Let m ≥ 2. Then:(A) If there exists k such that NP⊆ Σm TIME(nk)∩ Πm TIME(nk), then for every r there exists kr such that :(B) If there exists a superpolynomial time-constructible function f such that NTIME(f), then additionally .This strengthens a result by Mocas [M96] that for any r, .In addition, we use FM-truth definitions to give a simple sufficient condition for the arity hierarchy to be strict over finite models.

Construction of sheaves by tolerance relations

2016 ◽  
Vol 09 (02) ◽  
pp. 1650035 ◽  
Author(s):  
M. P. K. Kishore ◽  
R. V. G. Ravi Kumar ◽  
P. Vamsi Sagar
Keyword(s):  
Topological Space ◽  
Universal Algebra ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

In this paper a method to construct a global sheaf space over a topological space for an arbitrary set using tolerance relations is proposed. It is observed that in general, the sheaf constructed by this method is different from the sheaf constructed by the method discussed in [U. M. Swamy, Representation of Universal algebra by sheaves, Proc. Amer. Math. Soc. 45 (1974) 55–58]. A necessary and sufficient condition for embedding a non-empty set into the set of all global sections of a sheaf over given topological space is established, and further an application over graphs is studied.

On amalgamations of languages with Magidor-Malitz quantifiers

1979 ◽  
Vol 44 (4) ◽  
pp. 549-558
Author(s):  
Carl F. Morgenstern
Keyword(s):  
Universal Algebra ◽  
Model Theory ◽  
Natural Extension ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Free Variables ◽  
Countably Compact

In this paper we indicate how compact languages containing the Magidor-Malitz quantifiers Qκn in different cardinalities can be amalgamated to yield more expressive, compact languages.The language Lκ<ω, originally introduced by Magidor and Malitz [9], is a natural extension of the language L(Q) introduced by Mostowski and investigated by Fuhrken [6], [7], Keisler [8] and Vaught [13]. Intuitively, Lκ<ω is first-order logic together with quantifiers Qκn (n ∈ ω) binding n free variables which express “there is a set X of cardinality κ such than any n distinct elements of X satisfy …”, or in other words, iff the relation on determined by φ contains an n-cube of cardinality κ. With these languages one can express a variety of combinatorial statements of the type considered by Erdös and his colleagues, as well as concepts in universal algebra which are beyond the scope of first-order logic. The model theory of Lκ<ω has been further developed by Badger [1], Magidor and Malitz [10] and Shelah [12].We refer to a language as being < κ compact if, given any set of sentences Σ of the language, if Σ is finitely satisfiable and ∣Σ∣ < κ, then Σ has a model. The phrase countably compact is used in place of <ℵ1 compact.

scholarly journals Global Schauder decompositions of locally convex spaces

2007 ◽  
Vol 101 (1) ◽  
pp. 65
Author(s):  
Milena Venkova
Keyword(s):  
Convex Space ◽  
Entire Functions ◽  
Locally Convex Space ◽  
Locally Convex Spaces ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Locally Convex ◽  
Convex Spaces

We define global Schauder decompositions of locally convex spaces and prove a necessary and sufficient condition for two spaces with global Schauder decompositions to be isomorphic. These results are applied to spaces of entire functions on a locally convex space.

Automorphism Groups of Algebras of Finite Type

1972 ◽  
Vol 24 (6) ◽  
pp. 1065-1069 ◽  
Author(s):  
Matthew Gould
Keyword(s):  
Automorphism Group ◽  
Finite Number ◽  
Finite Type ◽  
Permutation Group ◽  
Universal Algebra ◽  
Automorphism Groups ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

By “algebra” we shall mean a finitary universal algebra, that is, a pair 〈A; F〉 where A and F are nonvoid sets and every element of F is a function, defined on A, of some finite number of variables. Armbrust and Schmidt showed in [1] that for any finite nonvoid set A, every group G of permutations of A is the automorphism group of an algebra defined on A and having only one operation, whose rank is the cardinality of A. In [6], Jónsson gave a necessary and sufficient condition for a given permutation group to be the automorphism group of an algebra, whereupon Plonka [8] modified Jonsson's condition to characterize the automorphism groups of algebras whose operations have ranks not exceeding a prescribed bound.

scholarly journals A new minimax theorem and a perturbed James's theorem

2002 ◽  
Vol 66 (1) ◽  
pp. 43-56 ◽  
Author(s):  
M. Ruiz Galán ◽  
S. Simons
Keyword(s):  
Bilinear Form ◽  
Convex Subset ◽  
Direct Proof ◽  
Minimax Theorem ◽  
Locally Convex Space ◽  
Sufficient Condition ◽  
Nonempty Convex Subset ◽  
Nonempty Convex ◽  
Locally Convex ◽  
Special Case

The main result of this paper is a sufficient condition for the minimax relation to hold for the canonical bilinear form on X × Y, where X is a nonempty convex subset of a real locally convex space and Y is a nonempty convex subset of its dual. Using the known “converse minimax theorem”, this result leads easily to a nonlinear generalisation of James's (“sup”) theorem. We give a brief discussion of the connections with the “sup-limsup theorem” and, in the appendix to the paper, we give a simple, direct proof (using Goldstine's theorem) of the converse minimax theorem referred to above, valid for the special case of a normed space.

scholarly journals The locally convex topology on the space of meromorphic functions

1995 ◽  
Vol 59 (3) ◽  
pp. 287-303 ◽  
Author(s):  
Karl-Goswin Grosse-Erdmann
Keyword(s):  
Meromorphic Functions ◽  
Main Tool ◽  
Positive Answer ◽  
Convex Topology ◽  
Projective Description ◽  
Space Of Meromorphic Functions ◽  
Locally Convex Topology ◽  
Locally Convex

AbstractWe give a positive answer to a question of Horst Tietz. A theorem of his that is related to the Mittag-Leffler theorem looks like a duality restult under some locally convex topology on the space of meromorphic functions. Tietz has posed the problem of finding such a topology. It is shown that a topology introduced by Holdguün in 1973 solves the problem. The main tool in the study of this topology is a projective description of it that is derived here. We also argue that Holdgrün's topology is the natural locally convex topology on the space of meromorphic functions.

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