scholarly journals Singularities of a construction of the $o$-completion of an Archimedean $\ell$-group with strong unit

1987 ◽  
Vol 37 (1) ◽  
pp. 1-3,4-6
Author(s):  
A. V. Koldunov
Keyword(s):  
Strong Unit

Examples of theories of presheaf type

2018 ◽  
Author(s):  
Olivia Caramello
Keyword(s):  
Finite Groups ◽  
Linear Independence ◽  
Geometric Theory ◽  
Vector Spaces ◽  
Linear Orders ◽  
Locally Finite ◽  
Strong Unit ◽  
Locally Finite Groups ◽  
Simplicial Sets ◽  
Separable Extensions

This chapter discusses several classical as well as new examples of theories of presheaf type from the perspective of the theory developed in the previous chapters. The known examples of theories of presheaf type that are revisited in the course of the chapter include the theory of intervals (classified by the topos of simplicial sets), the theory of linear orders, the theory of Diers fields, the theory of abstract circles (classified by the topos of cyclic sets) and the geometric theory of finite sets. The new examples include the theory of algebraic (or separable) extensions of a given field, the theory of locally finite groups, the theory of vector spaces with linear independence predicates and the theory of lattice-ordered abelian groups with strong unit.

scholarly journals Proses Desain Kursi dengan Memanfaatkan Modul Silinder dari Bonggol Jagung

2020 ◽  
pp. 1-10
Author(s):  
Priskila Saptorini ◽  
Andry Masri
Keyword(s):  
Design Process ◽  
Research Method ◽  
Professional Work ◽  
Strong Unit ◽  
Design Project ◽  
Corn Cobs ◽  
Compromise Value ◽  
The Right ◽  
Chair Design

One of the results of the exploration of corncobs is a cylindrical module. In this research, the cylindrical module will be used as a component in the chair, so that the search for the right technique and appropriate design will be made so that it can become a strong unit to be used as a chair. So, the purpose of this design process is to produce an appropriate chair design and in accordance with the techniques in utilizing cylindrical corncobs module, to get a compromise value from the novelty with module assembly techniques that must be able to function properly. The role of research for Design Project 5 and Professional Work is to find and test the material of corn cobs woven with rope as a component of a chair's seat base. The research method used was an experiment. The results showed a novelty and obtained a product made from corncobs in the form of a cylinder that can function well as a chair component.

scholarly journals From Freudenthal’s spectral theorem to projectable hulls of unital Archimedean lattice-groups, through compactifications of minimal spectra

2018 ◽  
Vol 30 (2) ◽  
pp. 513-526 ◽  
Author(s):  
Richard N. Ball ◽  
Vincenzo Marra ◽  
Daniel McNeill ◽  
Andrea Pedrini
Keyword(s):  
Explicit Construction ◽  
Continuous Functions ◽  
Spectral Theorem ◽  
Characteristic Functions ◽  
Prime Ideals ◽  
Minimal Extension ◽  
Strong Unit ◽  
Fundamental Relationship ◽  
Continuous Surjection ◽  
Archimedean Lattice

AbstractWe use a landmark result in the theory of Riesz spaces – Freudenthal’s 1936 spectral theorem – to canonically represent any Archimedean lattice-ordered groupGwith a strong unit as a (non-separating) lattice-group of real-valued continuous functions on an appropriateG-indexed zero-dimensional compactification{w_{G}Z_{G}}of its space{Z_{G}}ofminimalprime ideals. The two further ingredients needed to establish this representation are the Yosida representation ofGon its space{X_{G}}ofmaximalideals, and the well-known continuous surjection of{Z_{G}}onto{X_{G}}. We then establish our main result by showing that the inclusion-minimal extension of this representation ofGthat separates the points of{Z_{G}}– namely, the sublattice subgroup of{\operatorname{C}(Z_{G})}generated by the image ofGalong with all characteristic functions of clopen (closed and open) subsets of{Z_{G}}which are determined by elements ofG– is precisely the classical projectable hull ofG. Our main result thus reveals a fundamental relationship between projectable hulls and minimal spectra, and provides the most direct and explicit construction of projectable hulls to date. Our techniques do require the presence of a strong unit.

Lascar EL-WiFi-TH Data Logger

2020 ◽  
Vol 22 (1) ◽  
pp. 41-45
Author(s):  
Heather Parks
Keyword(s):  
Environmental Conditions ◽  
Cloud Service ◽  
Dew Point ◽  
Data Logger ◽  
Strong Unit ◽  
Data Loggers ◽  
Intended Use

The Lascar Data Logger system includes three parts: the data loggers, EasyLog WiFi Software, and the EasyLog Cloud service. The intended use is to monitor and record the temperature, humidity, and dew point of the space surrounding the data logger to aid in achieving optimal environmental conditions of the collection. While it is a strong unit, there are competitors that might be a better fit for an institution.

scholarly journals Representation of perfect and local MV-algebras

2011 ◽  
Vol 61 (3) ◽  
Author(s):  
Brunella Gerla ◽  
Ciro Russo ◽  
Luca Spada
Keyword(s):  
Unit Interval ◽  
Representation Theorems ◽  
Strong Unit ◽  
Mv Algebras

AbstractWe describe representation theorems for local and perfect MV-algebras in terms of ultraproducts involving the unit interval [0, 1]. Furthermore, we give a representation of local Abelian ℓ-groups with strong unit as quasi-constant functions on an ultraproduct of the reals. All the above theorems are proved to have a uniform version, depending only on the cardinality of the algebra to be embedded, as well as a definable construction in ZFC.The paper contains both known and new results and provides a complete overview of representation theorems for such classes.

scholarly journals Pseudo MV-algebras are intervals in ℓ-groups

2002 ◽  
Vol 72 (3) ◽  
pp. 427-446 ◽  
Author(s):  
Anatolij Dvurečenskij
Keyword(s):  
Strong Unit ◽  
Famous Result ◽  
Mv Algebra ◽  
Mv Algebras

AbstractWe show that any pseudo MV-algebra is isomorphic with an interval Γ(G, u), where G is an ℓ-group not necessarily Abelian with a strong unit u. In addition, we prove that the category of unital ℓ-groups is categorically equivalent with the category of pseudo MV-algebras. Since pseudo MV-algebras are a non-commutative generalization of MV-algebras, our assertions generalize a famous result of Mundici for a representation of MV-algebras by Abelian unital ℓ-groups. Our methods are completely different from those of Mundici. In addition, we show that any Archimedean pseudo MV-algebra is an MV-algebra.

scholarly journals The Poset of Primel-Ideals of an Abelianl-Group with a Strong Unit

1996 ◽  
Vol 184 (2) ◽  
pp. 604-612 ◽  
Author(s):  
Roberto Cignoli ◽  
Antoni Torrens
Keyword(s):  
Strong Unit
Sign in / Sign up

Export Citation Format

Share Document