Finitary Abstract Elementary Classes

The research in model theory has extended from the study of elementary classes to non-elementary classes, i.e. to classes which are not completely axiomatizable in elementary logic. The main theme has been the attempt to generalize tools from elementary stability theory to cover more applications arising in other branches of mathematics. In this doctoral thesis we introduce finitary abstract elementary classes, a non-elementary framework of model theory. These classes are a special case of abstract elementary classes (AEC), introduced by Saharon Shelah in the 1980's. We have collected a set of properties for classes of structures, which enable us to develop a 'geometric' approach to stability theory, including an independence calculus, in a very general framework. The thesis studies AEC's with amalgamation, joint embedding, arbitrarily large models, countable Löwenheim-Skolem number and finite character. The novel idea is the property of finite character, which enables the use of a notion of a weak type instead of the usual Galois type. Notions of simplicity, superstability, Lascar strong type, primary model and U-rank are inroduced for finitary classes. A categoricity transfer result is proved for simple, tame finitary classes: categoricity in any uncountable cardinal transfers upwards and to all cardinals above the Hanf number. Unlike the previous categoricity transfer results of equal generality the theorem does not assume the categoricity cardinal being a successor. The thesis consists of three independent papers. All three papers are joint work with Tapani Hyttinen.

A characterization of domains in C 2 with noncompact automorphism group

Let D be a bounded domain in C 2 with a non-compact group of holomorphic automorphisms. Model domains for D are obtained under the hypotheses that at least one orbit accumulates at a boundary point near which the boundary is smooth, real analytic and of finite type.

Domains in complex surfaces with non-compact automorphism groups

Let X be an arbitrary complex surface and D a domain in X that has a non-compact group of holomorphic automorphisms. A characterization of those domains D that admit a smooth, weakly pseudoconvex, finite type boundary orbit accumulation point is obtained.

Trade Blocs and the Cold War : The CMEA and the EC challenge, 1969-1976

The coherence of the Soviet bloc was seriously tested at the turn of the 1970s, as the Soviet Union and its allies engaged in intensive negotiations over their relations with the European Communities (EC). In an effort to secure their own national economic interests many East European countries began independent manoeuvres against the wishes of their bloc leader. However, much of the intra-bloc controversy was kept out of the public eye, as the battle largely took place behind the scenes, within the organisation for economic cooperation, the Council for Mutual Economic Assistance (CMEA). The CMEA policy-making process vis-à-vis the EC is described in this study with reference to primary archival materials. This study investigates the negotiating positions and powers of the CMEA member states in their efforts to deal with the economic challenge created by the progress of the EC, as it advanced towards the customs union. This entails an analysis of the functioning principles and performance of the CMEA machinery. The study traces the CMEA negotiations that began in 1970 over its policy toward the EC. The policy was finally adopted in 1974, and was followed by the first official meeting between the two organisations in early 1975. The story ends in 1976, when the CMEA s efforts to enter into working relations with the EC were seemingly frustrated by the latter. The first major finding of the study is that, contrary to much of the prior research, the Soviet Union was not in a hegemonic position vis-à-vis its allies. It had to use a lot of its resources to tame the independent manoeuvring of its smaller allies. Thus, the USSR was not the kind of bloc leader that the totalitarian literature has described. Because the Soviet Union had to spend so much attention on its own bloc-politics, it was not able to concentrate on formulating a policy vis-à-vis the EC. Thus, the Soviet leadership was dependent on its allies in those instances when the socialist countries needed to act as a bloc. This consequently opened up the possibility for the USSR s allies to manoeuvre. This study also argues that when the CMEA did manage to find a united position, it was a force that the EC had to reckon with in its policy-making. This was particularly the case in the implementation of the EC Common Commercial Policy. The other main finding of the study is that, although it has been largely neglected in the previous literature on the history of West European integration, the CMEA did in fact have an effect on EC decision-making. This study shows how for political and ideological reasons the CMEA members did not acknowledge the EC s supranational authority. Therefore the EC had no choice but to refrain from implementing its Common Commercial Policy in full.

Some Aspects of the Kobayashi and Carath,odory Metrics on Pseudoconvex Domains

The purpose of this article is to consider two themes, both of which emanate from and involve the Kobayashi and the Carath,odory metric. First, we study the biholomorphic invariant introduced by B. Fridman on strongly pseudoconvex domains, on weakly pseudoconvex domains of finite type in C (2), and on convex finite type domains in C (n) using the scaling method. Applications include an alternate proof of the Wong-Rosay theorem, a characterization of analytic polyhedra with noncompact automorphism group when the orbit accumulates at a singular boundary point, and a description of the Kobayashi balls on weakly pseudoconvex domains of finite type in C (2) and convex finite type domains in C (n) in terms of Euclidean parameters. Second, a version of Vitushkin's theorem about the uniform extendability of a compact subgroup of automorphisms of a real analytic strongly pseudoconvex domain is proved for C (1)-isometries of the Kobayashi and Carath,odory metrics on a smoothly bounded strongly pseudoconvex domain.

Expansions of tau hadronic spectral function moments in a nonpower QCD perturbation theory with tamed large order behavior

The moments of the hadronic spectral functions are of interest for the extraction of the strong coupling alpha(s) and other QCD parameters from the hadronic decays of the tau lepton. Motivated by the recent analyses of a large class of moments in the standard fixed-order and contour-improved perturbation theories, we consider the perturbative behavior of these moments in the framework of a QCD nonpower perturbation theory, defined by the technique of series acceleration by conformal mappings, which simultaneously implements renormalization-group summation and has a tame large-order behavior. Two recently proposed models of the Adler function are employed to generate the higher-order coefficients of the perturbation series and to predict the exact values of the moments, required for testing the properties of the perturbative expansions. We show that the contour-improved nonpower perturbation theories and the renormalization-group-summed nonpower perturbation theories have very good convergence properties for a large class of moments of the so-called ``reference model,'' including moments that are poorly described by the standard expansions. The results provide additional support for the plausibility of the description of the Adler function in terms of a small number of dominant renormalons.

Domains in complex surfaces with a noncompact automorphism group - II

Let X be an arbitrary complex surface and D subset of X a domain that has a noncompact group of holomorphic automorphisms. A characterization of those domains D that admit a smooth real analytic, finite type, boundary orbit accumulation point and whose closures are contained in a complete hyperbolic domain D' subset of X is obtained.

Investigations of the origin of stereocontrol in syndiospecific Ziegler-Natta polymerizations

In order to expand our understanding of the mechanism of stereocontrol in syndiospecific α-olefin polymerization, a family of Cs-symmetric, ansa-group 3 metallocenes was targeted as polymerization catalysts. The syntheses of new ansa-yttrocene and scandocene derivatives that employ the doubly [SiMe₂]- bridged ligand array (1,2-SiMe₂)₂{C₅H-3,5-(CHMe₂)₂} (where R = t- butyl, tBuThp; where R = i-propyl, iPrThp) are described. The structures of tBuThpY(µ-Cl)₂K(THF)₂, tBuThpSc(µ-Cl)₂K(Et₂O)₂, tBuThpYCH(SiMe₃)₂, Y₂{µ₂-(tBuThp)₂}(µ₂-H)₂, and tBuThpSc(µ-CH₃)₂ have been examined by single crystal X-ray diffraction methods. Ansa-yttrocenes and scandocenes that incorporate the singly [CPh₂]-bridged ligand array (CPh₂)(C₅H₄)(C₁₃H₈)(where C₅H₄ = Cp, cyclopentadienyl; where C₁₃H₈ = Flu, fluourenyl) have also been prepared. Select meallocene alkyl complexes are active single component catalysts for homopolymerization of propylene and 1-pentene. The scandocene tetramethylaluminate complexes generate polymers with the highes molecular weights of the series. Under all conditions examined atactic polymer microstructures are observed, suggesting a chain-end mechanism for stereocontrol.

A series of ansa-tantalocenes have been prepared as models for Ziegler-Natta polymerization catalysts. A singly bridged ansa-tantalocene trimethyl complex, Me₂Si(η⁵-C₅H₄)₂TaMe₃, has been prepared and used for the synthesis of a tantalocene ethylene-methyl complex. Addition of propylene to this ethylene-methyl adduct results in olefin exchange to give a mixture of endo and exo propylene isomers. Doubly-silylene bridged ansa-tantalocene complexes have been prepared with the tBuThp ligand; a tantalocene trimethyl complex and a tantalocene methylidene-methyl complex have been synthesized and characterized by X-ray diffraction. Thermolysis of the methylidene-methyl complex affords the corresponding ethylene-hydride complex. Addition of either propylene or styrene to this ethylene-hydride compound results in olefin exchange. In both cases, only one product isomer is observed. Studies of olefin exchange with ansa-tantalocene olefin-hydride and olefin-methyl complexes have provided information about the important steric influences for olefin coordination in Ziegler-Natta polymerization.

Structure theorems for noncommutative complete local rings

If R is a ring with identity, let N(R) denote the Jacobson radical of R. R is local if R/N(R) is an artinian simple ring and ∩N(R)ⁱ = 0. It is known that if R is complete in the N(R)-adic topology then R is equal to (B)_n, the full n by n matrix ring over B where E/N(E) is a division ring. The main results of the thesis deal with the structure of such rings B. In fact we have the following.

If B is a complete local algebra over F where B/N(B) is a finite dimensional normal extension of F and N(B) is finitely generated as a left ideal by k elements, then there exist automorphisms g_i,...,g_k of B/N(B) over F such that B is a homomorphic image of B/N[[x₁,…,x_k;g₁,…,g_k]] the power series ring over B/N(B) in noncommuting indeterminates x_i, where x_ib = g_i(b)x_i for all b ϵ B/N.

Another theorem generalizes this result to complete local rings which have suitable commutative subrings. As a corollary of this we have the following. Let B be a complete local ring with B/N(B) a finite field. If N(B) is finitely generated as a left ideal by k elements then there exist automorphisms g₁,…,g_k of a v-ring V such that B is a homomorphic image of V [[x₁,…,x_k;g₁,…,g_k]].

In both these results it is essential to know the structure of N(B) as a two sided module over a suitable subring of B.

Formal languages, part theory, and change

A general definition of interpreted formal language is presented. The notion “is a part of" is formally developed and models of the resulting part theory are used as universes of discourse of the formal languages. It is shown that certain Boolean algebras are models of part theory.

With this development, the structure imposed upon the universe of discourse by a formal language is characterized by a group of automorphisms of the model of part theory. If the model of part theory is thought of as a static world, the automorphisms become the changes which take place in the world. Using this formalism, we discuss a notion of abstraction and the concept of definability. A Galois connection between the groups characterizing formal languages and a language-like closure over the groups is determined.

It is shown that a set theory can be developed within models of part theory such that certain strong formal languages can be said to determine their own set theory. This development is such that for a given formal language whose universe of discourse is a model of part theory, a set theory can be imbedded as a submodel of part theory so that the formal language has parts which are sets as its discursive entities.

A educação como campo de batalha e local de seleção

Este trabalho é o resultado das reflexões relativas às leituras que venho realizando desde a minha graduação. A partir do entendimento de que a educação escolar, ao contrário de alguns de seus pressupostos, serviria especialmente à ordem social capitalista; sendo uma das maneiras mais eficientes de domesticar o ser humano. Não se trata de afirmar que toda educação escolar será sempre domesticadora, mas, que grande parte do seu trabalho acaba por contribuir para a diminuição da capacidade criativa do indivíduo. Entendo que a imposição da busca pela verdade e a tentativa de igualar a todos os indivíduos são julgamentos morais. Esses julgamentos representariam a interpretação da vida a partir de um ser enfraquecido, ou seja, teriam como função a preservação do decadente. Esses valores morais acabam por diminuir, também, a energia dos indivíduos que poderiam expandir-se. A escola pode ser um local onde o estudante poderá ter experiências capazes de levá-lo ao crescimento, ou não. Concordamos com Nietzsche, ao entender que há uma oposição entre a vontade de moral e a vontade de potência. O ser vivo quer crescer, ou preservar-se. A criação de novas formas de viver, de desejar uma vida com outra intensidade depende, dos instintos. A moral impõe ao indivíduo uma constante vigilância e coerção contra a expressão desses instintos. A energia que poderia gerar novas formas de viver, agora será utilizada contra o próprio indivíduo, atormentando-o. A escola ainda é uma fonte de experiências. Resta-nos saber como utilizá-la em seus potenciais criadores

Mersey & Weaver Fisheries Advisory Committee 16th September, 1974

This is the report from the Mersey and Weaver Fisheries Advisory Committee meeting, which was held on the 16th September 1974. The report looks at comments of the Regional Fisheries Officer on the report 'Taking Stock', and information including the aims of a report entitled 'Coarse Fisheries'. The report also includes a copy of the chairman's address to members of the Mersey and Weaver Anglers' Consultative Association, and the report by the Unit Water Quality Officer on fisheries activities. This covers general fisheries management work, stocking and biological work carried out including the Rivers Tame and Bollin, and fish mortalities listed by cause. The Fisheries Advisory Committee was part of the Regional Water Authorities, in this case the North West Water Authority. This preceded the Environment Agency which came into existence in 1996.

Mersey & Weaver Fisheries Advisory Committee 22nd October, 1975.

This is the report from the Mersey and Weaver Fisheries Advisory Committee meeting, which was held on the 22nd October 1975. The report contains information on a report by the divisional scientist on fisheries activities, importation of live freshwater fish, drainage representation on local committees, new byelaws and fishing licence duties. The report by the divisional scientist looks at permissions for stocking and electrofishing, biological work and results of fish toxicity tests carried out in Rivers Bollin, Etherow, Glaze and Tame. It also contains records of fish mortalities. The Fisheries Advisory Committee was part of the Regional Water Authorities, in this case the North West Water Authority. This preceded the Environment Agency which came into existence in 1996.

Mersey & Weaver Fisheries Advisory Committee 21st April, 1975

This is the report from the Mersey and Weaver Fisheries Advisory Committee meeting, which was held on the 21st April, 1975. It covers information on fishery byelaws, and a report by Unit Water Quality Officer on fisheries activities. This section includes work on fisheries management, stocking carried out, biological work carried out on the Rivers Bollin, Etherow, Goyt, Tame, Glaze and Roch and information on the mortality of coarse fish in the Rochdale Canal. Other areas looked at include licence duties and inportation of live freshwater fish. The Fisheries Advisory Committee was part of the Regional Water Authorities, in this case the North West Water Authority. This preceded the Environment Agency which came into existence in 1996.

Mersey & Weaver Fisheries Advisory Committee 27th October, 1976.

This is the report from the Mersey and Weaver Fisheries Advisory Committee meeting, which was held on the 27th October, 1976. The report contains sections on fish stocking, fisheries activities, weed growth in the River Weaver, pollution incidents and the drought situation. The section on fish stocking includes background information about fish stocking by the authority; difficulties; migratory fish; stocking after pollution; stocking of Waters within the Region; stocking with coarse fish; and recommendations. The section on fisheries activities includes fish mortalities and biological work on the River Tame, Goyt, Weaver, Mersey, Dane, Dean, and Gowy. The Fisheries Advisory Committee was part of the Regional Water Authorities, in this case the North West Water Authority. This preceded the Environment Agency which came into existence in 1996.