Limit ultrapowers and abstract logics

1987 ◽  
Vol 52 (2) ◽  
pp. 437-454 ◽  
Author(s):  
Paolo Lipparini
Keyword(s):  
Interpolation Property ◽  
Finite Cover ◽  
Abstract Logic ◽  
Superstable Theory ◽  
Proper Extension ◽  
Elementary Classes ◽  
Abstract Logics ◽  
Countable Models

AbstractWe associate with any abstract logic L a family F(L) consisting, intuitively, of the limit ultrapowers which are complete extensions in the sense of L.For every countably generated [ω, ω]-compact logic L, our main applications are:(i) Elementary classes of L can be characterized in terms of ≡L only.(ii) If and are countable models of a countable superstable theory without the finite cover property, then .(iii) There exists the “largest” logic M such that complete extensions in the sense of M and L are the same; moreover M is still [ω, ω]-compact and satisfies an interpolation property stronger than unrelativized ⊿-closure.(iv) If L = Lωω(Qx), then cf(ωx) > ω and λω < ωx, for all λ < ωx.We also prove that no proper extension of Lωω generated by monadic quantifiers is compact. This strengthens a theorem of Makowsky and Shelah. We solve a problem of Makowsky concerning Lκλ-compact cardinals. We partially solve a problem of Makowsky and Shelah concerning the union of compact logics.

A first approach to abstract modal logics

1989 ◽  
Vol 54 (3) ◽  
pp. 1042-1062 ◽  
Author(s):  
Josep M. Font ◽  
Ventura Verdú
Keyword(s):  
Modal Logic ◽  
Inference Rule ◽  
Heyting Algebras ◽  
Abstract Concepts ◽  
Algebraic Models ◽  
Abstract Logic ◽  
Sequent Systems ◽  
Abstract Logics ◽  
Set Up ◽  
Modal Systems

AbstractThe object of this paper is to make a study of four systems of modal logic (S4, S5, and their intuitionistic analogues IM4 and IM5) with the techniques of the theory of abstract logics set up by Suszko, Bloom, Brown, Verdú and others. The abstract concepts corresponding to such systems are defined as generalizations of the logics naturally associated to their algebraic models (topological Boolean or Heyting algebras, general or semisimple). By considering new suitably defined connectives and by distinguishing between having the rule of necessitation only for theorems or as a full inference rule (which amounts to dealing with all filters or with open filters of the algebras) we are able to reduce the study of a modal (abstract) logic L to that of two nonmodal logics L− and L+ associated with L. We find that L is “of IM4 type” if and only if L− and L+ are both intuitionistic and have the same theorems, and logics of type S4, IM5 or S5 are obtained from those of type IM4 simply by making classical L−, L+ or both. We compare this situation with that found in recent approaches to intuitionistic modal logic using birelational models or using higher-level sequent-systems. The treatment of modal systems with abstract logics is rather new, and in our way to it we find several general constructions and results which can also be applied to other modal systems weaker than those we study in detail.

The metamathematics of model theory: Discovering language in action

1981 ◽  
Vol 46 (3) ◽  
pp. 490-498
Author(s):  
Douglas E. Miller
Keyword(s):  
Topological Space ◽  
Model Theory ◽  
First Order ◽  
Elementary Classes ◽  
Countable Models

AbstractWe discuss the problem of defining the collection of first-order elementary classes in terms of the natural topological space of countable models.

Geometry of *-Finite Types

1999 ◽  
Vol 64 (4) ◽  
pp. 1375-1395 ◽  
Author(s):  
Ludomir Newelski
Keyword(s):  
Algebraic Group ◽  
Division Ring ◽  
Algebraic Groups ◽  
Superstable Theory ◽  
Countable Models

AbstractAssume T is a superstable theory with < 2ℵ0 countable models. We prove that any *- algebraic type of -rank > 0 is m-nonorthogonal to a *-algebraic type of -rank 1. We study the geometry induced by m-dependence on a *-algebraic type p* of -rank 1. We prove that after some localization this geometry becomes projective over a division ring . Associated with p* is a meager type p. We prove that p is determined by p* up to nonorthogonality and that underlies also the geometry induced by forking dependence on any stationarization of p. Also we study some *-algebraic *-groups of -rank 1 and prove that any *-algebraic *-group of -rank 1 is abelian-by-finite.

Flat Morley sequences

1999 ◽  
Vol 64 (3) ◽  
pp. 1261-1279
Author(s):  
Ludomir Newelski
Keyword(s):  
Superstable Theory ◽  
Complete Type ◽  
Finite Set ◽  
Countable Models

AbstractAssume T is a small superstable theory. We introduce the notion of a flat Morley sequence, which is a counterpart of the notion of an infinite Morley sequence in a type p, in case when p is a complete type over a finite set of parameters. We show that for any flat Morley sequence Q there is a model M of T which is τ-atomic over {Q}. When additionally T has few countable models and is 1-based, we prove that within M there is an infinite Morley sequence I, with I ⊂ dcl(Q), such that M is prime over I.

USING THE TECHNOLOGY OF DEVELOPING CRITICAL THINKING AT UKRAINIAN LESSONS IN ELEMENTARY CLASSES

2018 ◽  
Vol 2 (21) ◽  
pp. 51-56
Author(s):  
S.M. Dubiaha ◽  
◽  
Y.O. Saienko ◽  
V.I. Dubiaha ◽  
◽  
...  
Keyword(s):  
Critical Thinking ◽  
Elementary Classes

Incentives of the State to promote the retrofitting of the agricultural sector: Regional considerations

2020 ◽  
Vol 16 (6) ◽  
pp. 1101-1113
Author(s):  
M.Sh. Gutuev ◽  
B.Sh. Ibragimova
Keyword(s):  
Agricultural Sector ◽  
Animal Husbandry ◽  
Technological Equipment ◽  
Agricultural Producers ◽  
Agricultural Technologies ◽  
Abstract Logic ◽  
Land Cultivation ◽  
Equipment Acquisition ◽  
Acquisition Costs ◽  
The Republic

Subject. The article discusses the availability of technological equipment in the agriculture of the Republic of Dagestan. Objectives. We analyze the current situation and trends in the development of available technological equipment in the republican agriculture, identify the role and place of machine and tractor fleet in the retrofitting of the regional agriculture. Methods. The study is based on monographic, abstract logic, statistical, analytical methods. Results. Dagestan has got a critically few technological equipment, which affects the development of the regional agricultural sector. The availability of technological equipment is found to have dramatically reduced in animal husbandry for the recent 30 years. The availability of technological equipment and land cultivation strongly correlates, thus simplifying applicable agricultural technologies. Most agricultural producers of Dagestan were found to be unable to participate in the program for federal agricultural lease. Conclusions and Relevance. The deterioration of available technological equipment in agriculture is a key cause undermining the competitiveness of products and efficiency of the regional agriculture. We prove the importance of governmental actions incentivizing the influx of new technological equipment, including a set of measures reinforcing the availability of technological equipment. As long as most agricultural producers are microbusinesses that lack resources to participate in many machine renovation programs, funding should be increased substantially to subsidize a portion of equipment acquisition costs incurred by agricultural producers, and a portion of reimbursed costs as much as at least 50 percent of the value of agricultural machines acquired.

Propriété contre possession: les conflits liés aux plantations industrielles d'arbres | Property rights vs. common law possession: conflicts surrounding industrial tree plantations

2007 ◽  
Vol 158 (3-4) ◽  
pp. 65-69 ◽  
Author(s):  
Julien-François Gerber ◽  
Rolf Steppacher
Keyword(s):  
Property Rights ◽  
Common Law ◽  
Sustainable Use ◽  
Institutional Logics ◽  
Local Communities ◽  
Tree Plantations ◽  
Ecological Interactions ◽  
Abstract Logic ◽  
Property Versus ◽  
Concrete Logic

This article proposes a new way of looking at social conflicts relating to industrial tree plantations by arguing that such conflicts reflect the struggle between two distinct institutional logics, i.e., property versus possession. The abstract logic of property, enhanced by credit relations and the minimization of costs, stimulates commercial plantations and tends to be detrimental to the environment. By contrast, the concrete logic of possession forces local communities to take account of complex local social and ecological interactions, and thereby encourages a sustainable use of the forest.

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