Some model theory of the Heisenberg group: I. Unitriangular representations of models of a subtheory of its universal theory

2020 ◽  
pp. 33-46
Keyword(s):  
Heisenberg Group ◽  
Model Theory ◽  
Universal Theory ◽  
Group I

From “Metabelian ℚ-Vector Spaces” to New ω-Stable Groups

1996 ◽  
Vol 2 (1) ◽  
pp. 84-93 ◽  
Author(s):  
Olivier Chapuis
Keyword(s):  
Group Theory ◽  
Model Theory ◽  
Stability Theory ◽  
Abelian Groups ◽  
Vector Spaces ◽  
Universal Theory ◽  
Direct Power ◽  
Metabelian Groups ◽  
Free Abelian Groups ◽  
Torsion Free

The aim of this paper is to describe (without proofs) an analogue of the theory of nontrivial torsion-free divisible abelian groups for metabelian groups. We obtain illustrations for “old-fashioned” model theoretic algebra and “new” examples in the theory of stable groups. We begin this paper with general considerations about model theory. In the second section we present our results and we give the structure of the rest of the paper. Most parts of this paper use only basic concepts from model theory and group theory (see [14] and especially Chapters IV, V, VI and VIII for model theory, and see for example [23] and especially Chapters II and V for group theory). However, in Section 5, we need some somewhat elaborate notions from stability theory. One can find the beginnings of this theory in [14], and we refer the reader to [16] or [21] for stability theory and to [22] for stable groups.§1. Some model theoretic considerations. Denote by the theory of torsion-free abelian groups in the language of groups ℒgp. A finitely generated group G satisfies iff G is isomorphic to a finite direct power of ℤ. It follows that axiomatizes the universal theory of free abelian groups and that the theory of nontrivial torsion-free abelian groups is complete for the universal sentences. Denote by the theory of nontrivial divisible torsion-free abelian groups.

Flag algebras

2007 ◽  
Vol 72 (4) ◽  
pp. 1239-1282 ◽  
Author(s):  
Alexander A. Razborov
Keyword(s):  
Model Theory ◽  
Simple Proof ◽  
Edge Density ◽  
Universal Theory ◽  
Extremal Combinatorics ◽  
Finite Models ◽  
Flag Algebras ◽  
Formal Calculus ◽  
And Function

AbstractAsymptotic extremal combinatorics deals with questions that in the language of model theory can be re-stated as follows. For finite models M, N of an universal theory without constants and function symbols (like graphs, digraphs or hypergraphs), let p(M, N) be the probability that a randomly chosen sub-model of N with ∣M∣ elements is isomorphic to M. Which asymptotic relations exist between the quantities p(M1,N),…, p(Mh,N), where M1,…, M1, are fixed “template” models and ∣N∣ grows to infinity?In this paper we develop a formal calculus that captures many standard arguments in the area, both previously known and apparently new. We give the first application of this formalism by presenting a new simple proof of a result by Fisher about the minimal possible density of triangles in a graph with given edge density.

Ultrastructural Lesions Produced by Alcohol and Sucrose in the Heart and Liver of C57BL Mice

1970 ◽  
Vol 28 ◽  
pp. 208-209
Author(s):  
K.K. SEKHRI ◽  
C.S. ALEXANDER ◽  
H.T. NAGASAWA
Keyword(s):  
Osmium Tetroxide ◽  
Male Mice ◽  
Alcohol Group ◽  
Group Iii ◽  
Group I ◽  
C57bl Mice ◽  
Group Ii

C57BL male mice (Jackson Lab., Bar Harbor, Maine) weighing about 18 gms were randomly divided into three groups: group I was fed sweetened liquid alcohol diet (modified Schenkl) in which 36% of the calories were derived from alcohol; group II was maintained on a similar diet but alcohol was isocalorically substituted by sucrose; group III was fed regular mouse chow ad lib for five months. Liver and heart tissues were fixed in 2.5% cacodylate buffered glutaraldehyde, post-fixed in 2% osmium tetroxide and embedded in Epon-araldite.

The Quantitative Ultrastructure of the Heart Muscle of Japanese Quail by Hypergravitation, Hypodynamy and Combination

1990 ◽  
Vol 48 (3) ◽  
pp. 188-189
Author(s):  
Anton Bózner ◽  
Mikuláš Gažo ◽  
Jozef Dostál
Keyword(s):  
Japanese Quail ◽  
Heart Muscle ◽  
Relative Size ◽  
Combination Group ◽  
Control Group ◽  
Group V ◽  
Group Iii ◽  
Space Flights ◽  
Group I ◽  
Quantitative Ultrastructure

It is anticipated that Japanese quail /Coturnix coturnix japonica/ will provide animal proteins in long term space flights. Consequently this species of birds is of research interest of international space program INTERCOSMOS. In the year 1987 we reported on an experiment /2/ in which the effect of chronic acceleration of 2 G hypergravitation, the hypodynamy and the simultaneous effect of chronic acceleration and the location in the centre of the turntable of the centrifuge on the protein fractions in skeletal muscles was studied. The ultrastructure of the heart muscle was now in this experiments examined as well.Japanese quail cockerels, aged 48 days were exposed to 2 G hypergravitation /group IV/ in a 6,4 m diameter centrifuge, to hypodynamy /group III/ and their combination /group V/, respectively for 6 days / Fig.1/. The hypodynamy in group III was achieved by suspending the birds in jackets without contact the floor. The group II was located in the centre ofthe turntable of the centrifuge. The control group I. was kept under normal conditions. The quantitative ultrastructure of myocard was evaluated by the methods of Weibel/3/ - this enables to determine the number, relative size and volume of mitochondria volume of single mitochondria, defficiency of mitochondrial cristae and volume of myofibrils.

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