Filtral powers of structures

1998 ◽  
Vol 63 (4) ◽  
pp. 1239-1254 ◽  
Author(s):  
P. Ouwehand ◽  
H. Rose
Keyword(s):  
Elementary Substructure ◽  
Elementary Class ◽  
Reduced Products ◽  
Amalgamation Class ◽  
Finite Products

AbstractAmong the results of this paper are the following:1. Every Boolean (ultra)power is the union of an updirected elementary family of direct ultrapowers.2. Under certain conditions, a finitely iterated Boolean ultrapower is isomorphic to a single Boolean ultrapower.3. A ω-bounded filtral power is an elementary substructure of a filtral power.4. Let be an elementary class closed under updirected unions (e.g., if is an amalgamation class); then is closed under finite products if and only if is closed under reduced products if and only if is a Horn class.

Comparative studies regarding the use of recycled PVC in finite products

2017 ◽  
Vol 62 (2) ◽  
pp. 45-52
Author(s):  
Zosin Sergiu Petri ◽  
◽  
Dumitru Ristoiu ◽  
Mihail Simion Beldean-Galea ◽  
Radu Mihăiescu ◽  
...  
Keyword(s):  
Comparative Studies ◽  
Finite Products

Theory of models with generalized atomic formulas

1960 ◽  
Vol 25 (1) ◽  
pp. 1-26 ◽  
Author(s):  
H. Jerome Keisler
Keyword(s):  
Natural Number ◽  
Finite Sequence ◽  
Sufficient Condition ◽  
Elementary Extension ◽  
Necessary And Sufficient Condition ◽  
Elementary Class ◽  
Relational Systems ◽  
Necessary And Sufficient

IntroductionWe shall prove the following theorem, which gives a necessary and sufficient condition for an elementary class to be characterized by a set of sentences having a prescribed number of alternations of quantifiers. A finite sequence of relational systems is said to be a sandwich of order n if each is an elementary extension of (i ≦ n—2), and each is an extension of (i ≦ n—2). If K is an elementary class, then the statements (i) and (ii) are equivalent for each fixed natural number n.

Finitely generic models of TUH, for certain model companionable theories T

1985 ◽  
Vol 50 (3) ◽  
pp. 604-610
Author(s):  
Francoise Point
Keyword(s):  
Discriminator Variety ◽  
Generic Models ◽  
Elementary Class ◽  
Ordered Groups ◽  
Existentially Closed ◽  
Closed Element ◽  
Starting Point ◽  
Joint Embedding ◽  
Joint Embedding Property ◽  
Generic Elements

The starting point of this work was Saracino and Wood's description of the finitely generic abelian ordered groups [S-W].We generalize the result of Saracino and Wood to a class ∑UH of subdirect products of substructures of elements of a class ∑, which has some relationships with the discriminator variety V(∑t) generated by ∑. More precisely, let ∑ be an elementary class of L-algebras with theory T. Burris and Werner have shown that if ∑ has a model companion then the existentially closed models in the discriminator variety V(∑t) form an elementary class which they have axiomatized. In general it is not the case that the existentially closed elements of ∑UH form an elementary class. For instance, take for ∑ the class ∑0 of linearly ordered abelian groups (see [G-P]).We determine the finitely generic elements of ∑UH via the three following conditions on T:(1) There is an open L-formula which says in any element of ∑UH that the complement of equalizers do not overlap.(2) There is an existentially closed element of ∑UH which is an L-reduct of an element of V(∑t) and whose L-extensions respect the relationships between the complements of the equalizers.(3) For any models A, B of T, there exists a model C of TUH such that A and B embed in C.(Condition (3) is weaker then “T has the joint embedding property”. It is satisfied for example if every model of T has a one-element substructure. Condition (3) implies that ∑UH has the joint embedding property and therefore that the class of finitely generic elements of ∑UH is complete.)

scholarly journals ON PRODUCTS OF ELEMENTARILY INDIVISIBLE STRUCTURES

2016 ◽  
Vol 81 (3) ◽  
pp. 951-971
Author(s):  
NADAV MEIR
Keyword(s):  
New Products ◽  
Elementary Substructure ◽  
First Order ◽  
Order Language ◽  
Image Position

AbstractWe say a structure ${\cal M}$ in a first-order language ${\cal L}$ is indivisible if for every coloring of its universe in two colors, there is a monochromatic substructure ${\cal M}\prime \subseteq {\cal M}$ such that ${\cal M}\prime \cong {\cal M}$. Additionally, we say that ${\cal M}$ is symmetrically indivisible if ${\cal M}\prime$ can be chosen to be symmetrically embedded in ${\cal M}$ (that is, every automorphism of ${\cal M}\prime$ can be extended to an automorphism of ${\cal M}$). Similarly, we say that ${\cal M}$ is elementarily indivisible if ${\cal M}\prime$ can be chosen to be an elementary substructure. We define new products of structures in a relational language. We use these products to give recipes for construction of elementarily indivisible structures which are not transitive and elementarily indivisible structures which are not symmetrically indivisible, answering two questions presented by A. Hasson, M. Kojman, and A. Onshuus.

On the mechanism of formation of dimeric and reduced products from an α-halo amide with sodium methoxide

Tetrahedron ◽  
1978 ◽  
Vol 34 (15) ◽  
pp. 2371-2375 ◽  
Author(s):  
Gy. Simig ◽  
K. Lempert ◽  
Zs. Váli ◽  
G. Tóth ◽  
J. Tamás
Keyword(s):  
Sodium Methoxide ◽  
Mechanism Of Formation ◽  
Reduced Products

Closed form evaluation of sums containing squares of Fibonomial coefficients

2016 ◽  
Vol 66 (3) ◽  
Author(s):  
Emrah Kiliç ◽  
Helmut Prodinger
Keyword(s):  
Closed Form ◽  
Systematic Approach ◽  
Sums Of Squares ◽  
Lucas Numbers ◽  
Fibonomial Coefficients ◽  
Finite Products ◽  
Fibonacci And Lucas Numbers ◽  
Form Evaluation

AbstractWe give a systematic approach to compute certain sums of squares of Fibonomial coefficients with finite products of generalized Fibonacci and Lucas numbers as coefficients. The technique is to rewrite everything in terms of a variable

Sign in / Sign up

Export Citation Format

Share Document