The Ontological Import of Adding Proper Classes

In this article, we analyse the ontological import of adding classes to set theories. We assume that this increment is well represented by going from ZF system to NBG. We thus consider the standard techniques of reducing one system to the other. Novak proved that from a model of ZF we can build a model of NBG (and vice versa), while Shoenfield have shown that from a proof in NBG of a set-sentence we can generate a proof in ZF of the same formula. We argue that the first makes use of a too strong metatheory. Although meaningful, this symmetrical reduction does not equate the ontological content of the theories. The strong metatheory levels the two theories. Moreover, we will modernize Shoenfields proof, emphasizing its relation to Herbrands theorem and that it can only be seen as a partial type of reduction. In contrast with symmetrical reductions, we believe that asymmetrical relations are powerful tools for comparing ontological content. In virtue of this, we prove that there is no interpretation of NBG in ZF, while NBG trivially interprets ZF. This challenges the standard view that the two systems have the same ontological content

Une approche axiomatique du forcing et des extensions génériques

This paper provides a conceptual analysis of forcing and generic extensions. Our goal is to give general axioms for the concept of standard forcing-generic extension and to show that the usual (poset) constructions are unified and explained as realizations of this concept. According to our approach, the basic idea behind forcing and generic extensions is that the latter are uniform adjunctions which are groundcontrolled by forcing, and forcing is nothing more than that ground-control. As a result of our axiomatization of this idea, the usual definitions of forcing and genericity are derived.Cet article présente une analyse conceptuelle du forcing et des extensions génériques. Notre objectif est de donner des axiomes généraux pour le concept d’extension forcing-générique standard, et de montrer que les constructions habituelles sont unifiées et expliquées comme étant des réalisations de ce concept. Selon notre approche, l’idée-clé sous-tendant le forcing et les extensions génériques est que ces dernières sont des adjonctions uniformes qui sont contrôlées par le forcing, ainsi le forcing n’est rien de plus que ce contrôle. Comme conséquence de notre axiomatisation de cette idée, on dérive les définitions habituelles du forcing et de la généricité

The foudations of mathematical thought in the twentieth century and the foundational relevance of model theory

Orientador: Walter Alexandre CarnielliTese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias HumanasResumo: Esta Tese tem como objetivo elucidar, ao menos parcialmente, a questão do significado da Teoria de Modelos para uma reflexão sobre o conhecimento matemático no século XX. Para isso, vamos buscar, primeiramente, alcançar uma compreensão da própria reflexão sobre o conhecimento matemático, que será denominada de Fundamentos do Pensamento Matemático no século XX, e da própria relevância fundacional. Em seguida, analisaremos, dentro do contexto fundacional estabelecido, o papel da Teoria de Modelos e da sua interação com a Álgebra, em geral, e, finalmente, empreenderemos um estudo de caso específico. Nesse estudo de caso mostraremos que a Teoria de Galois pode ser vista como um conteúdo lógico, e buscaremos compreender o significado fundacional desse enquadramento modelo-teórico para uma parte da Álgebra clássica.Abstract: The aim of the present Thesis is to bring some light to the question about the status and relevance of Model Theory to a reflection about the mathematical knowledge in the twentieth century. To pursue this target, we will, first of all, try to reach a comprehension of the reflection about the mathematical knowledge, itself, what will be designated as Foundations of Mathematical Thought in the twentieth century, and of the foundational relevance, itself. In the sequel, we will provide an analysis, of the role of Model Theory and its interaction with Algebra, in general, within the established foundational setting and, finally, we will discuss a specific study case. In this study case we will show that Galois Theory can be seen as a logical content, and we will try to understand the foundational meaning of this model-theoretic framework for some part of classical Algebra.DoutoradoLogicaDoutor em Filosofi

Interação Embalagem-alimento Sobre A Estabilidade De Doce De Cupuaçu (theobroma Grandiflorum Schum.)

Cupuaçu (Theobroma grandiflorum Schum.) is an exotic fruit with a promising economic potential, particularly due to its strong aroma and creamy texture. This study aimed to produce sweetened cupuaçu puree and evaluate the effects of packaging corrosion on its sensory properties and shelf-life in tinplated cans. After 240 days of storage, the commercially sterile product had average sensory analysis scores of 5.89 ± 0.21, 5.39 ± 0.30, 5.45 ± 0.21 and 5.49 ± 0.25, for appearance, aroma, flavor and overall appreciation, respectively. Sensory acceptance scores did not change during storage (p>0.05). Corrosion potential and low tin and iron levels in the product, which are parameters used to evaluate food-packaging interaction, demonstrated the product remained food-safe throughout its shelf-life. Tinplate is a promising packaging material for sweetened cupuaçu puree due to its mechanical and protective properties. Furthermore, tin plating is an economically viable food technology to extend the shelf-life of cupuaçu products and expand its domestic and international markets.2941006101

Vortices in superconductors with a columnar defect: finite size effects

In the present work we investigate the behavior of a vortex in a long superconducting cylinder near to a columnar defect at the center. The derivations of the local magnetic field distribution and the Gibbs free energy will be carried out for a cylinder and a cavity of arbitrary sizes. From the general expressions, it considered two particular limits: one in which the radius of the cavity is very small but the radius of the superconducting cylinder is kept finite; and one in which the radius of the superconducting cylinder is taken very large (infinite) but the radius of the cavity is kept finite. In both cases the maximum number of vortices which are allowed in the cavity is determined. In addition, the surface barrier field for flux entrance into the cavity is calculated.Comment: 13 pages, 1 figur

Food-packaging Interaction On The Stability Of Canned Sweetened Cupuacu (theobroma Grandiflorum Schum.) Puree

Cupuacu (Theobroma grandiflorum Schum.) is an exotic fruit with a promising economic potential, particularly due to its strong aroma and creamy texture. This study aimed to produce sweetened cupuacu puree and evaluate the effects of packaging corrosion on its sensory properties and shelf-life in tinplated cans. After 240 days of storage, the commercially sterile product had average sensory analysis scores of 5.89 +/- 0.21, 5.39 +/- 0.30, 5.45 +/- 0.21 and 5.49 +/- 0.25, for appearance, aroma, flavor and overall appreciation, respectively. Sensory acceptance scores did not change during storage (p>0.05). Corrosion potential and low tin and iron levels in the product, which are parameters used to evaluate food-packaging interaction, demonstrated the product remained food-safe throughout its shelf-life. Tinplate is a promising packaging material for sweetened cupuacu puree due to its mechanical and protective properties. Furthermore, tin plating is an economically viable food technology to extend the shelf-life of cupuacu products and expand its domestic and international markets.2941006101

FOOD-PACKAGING INTERACTION ON THE STABILITY OF CANNED SWEETENED CUPUAÇU (Theobroma grandiflorum Schum.) PUREE

Cupuaçu ( Theobroma grandiflorum Schum.) is an exotic fruit with a promising economic potential, particularly due to its strong aroma and creamy texture. This study aimed to produce sweetened cupuaçu puree and evaluate the effects of packaging corrosion on its sensory properties and shelf - life in tinplated cans. After 240 days of storage, the commercially sterile product had average sensory analysis scores of 5.89 ± 0.21, 5.39 ± 0.30, 5.45 ± 0.21 and 5.49 ± 0.25, for appearance, aroma, flavor and overall appreciation, respectively. Sensory acceptance scores did not change during storage (p>0.05). Corrosion potential and low tin and iron levels in the product, which are parameters used to evaluate food - packaging interaction, demonstrated the product remained food - safe throughout its shelf - life. Tinplate is a promising packaging material for sweetened cupuaçu puree due to its mechanical and protective properties. Furthermore, tin plating is an economically viable food technology to extend the shelf - life of cupuaçu products and expand its domestic and international markets