O objetivo deste trabalho é apresentar a versão carrolliana de dois paradoxos clássicos e um original, acompanhadas da reconstrução e exame do tratamento lógico oferecido por Carroll e de como tais paradoxos foram tratados por outros autores.

We define an $\mathfrak{R}$-group to be a stable group with the property that a generic element can only be algebraic over a generic. We then derive some corollaries for $\mathfrak{R}$-groups and fields, and prove a decomposition theorem and a field theorem. As a nonsuperstable example, we prove that small stable groups are $\mathfrak{R}$-groups.

We prove that a stable solvable group $G$ which satisfies $x^n = 1$ generically is of finite exponent dividing some power of $n$. Furthermore, $G$ is nilpotent-by-finite. A second result is that in a stable group of finite exponent, involutions either have big centralisers, or invert a subgroup of finite index (which hence has to be abelian).

Mazur & Booth present an intriguing model of the relationship between circulating testosterone levels and dominance behaviour in man, but their review of studies on testosterone–behaviour relationships in man is selective. Much of the evidence they cite is correlational in nature. Placebo-controlled manipulations of testosterone levels are required to test their hypothesis that dominance levels are testosterone-dependent in man. The changes in testosterone level that follow behavioural experience may be a consequence of stress. Testosterone levels in man are determined by (...) a wide variety of factors, and a multivariate approach is required. (shrink)

The following theorems are proved about the Frattini-free componentG Φ of a soluble stable ℜ-group: a) If it has a normal subgroupN with nilpotent quotientG Φ/N, then there is a nilpotent subgroupH ofG Φ withG Φ=NH. b) It has Carter subgroups; if the group is small, they are all conjugate. c) Nilpotency modulo a suitable Frattini-subgroup (to be defined) implies nilpotency. The last result makes use of a new structure theorem for the centre of the derivative of the Frattini-free component (...) of a centreless soluble ℜ-group. (shrink)

We define an R-group to be a stable group with the property that a generic element (for any definable transitive group action) can only be algebraic over a generic. We then derive some corollaries for R-groups and fields, and prove a decomposition theorem and a field theorem. As a nonsuperstable example, we prove that small stable groups are R-groups.

A minimal field of non-zero characteristic is algebraically closed.

This document presents the Bonn PRINTEGER Consensus Statement: Working with Research Integrity—Guidance for research performing organisations. The aim of the statement is to complement existing instruments by focusing specifically on institutional responsibilities for strengthening integrity. It takes into account the daily challenges and organisational contexts of most researchers. The statement intends to make research integrity challenges recognisable from the work-floor perspective, providing concrete advice on organisational measures to strengthen integrity. The statement, which was concluded February 7th 2018, provides guidance on (...) the following key issues: § 1.Providing information about research integrity § 2.Providing education, training and mentoring § 3.Strengthening a research integrity culture § 4.Facilitating open dialogue § 5.Wise incentive management § 6.Implementing quality assurance procedures § 7.Improving the work environment and work satisfaction § 8.Increasing transparency of misconduct cases § 9.Opening up research § 10.Implementing safe and effective whistle-blowing channels § 11.Protecting the alleged perpetrators § 12.Establishing a research integrity committee and appointing an ombudsperson § 13.Making explicit the applicable standards for research integrity. (shrink)

We generalise various properties of quasiendomorphisms from groups with regular generic to small abelian groups. In particular, for a small abelian group such that no infinite definable quotient is connected-by-finite, the ring of quasi-endomorphisms is locally finite. Under some additional assumptions, it decomposes modulo some nil ideal into a sum of finitely many matrix rings.

We define a generalized version of CM-triviality, and show that in the presence of enough regular types, or solubility, a stable CM-trivial group is nilpotent-by-finite. A torsion-free small CM-trivial stable group is abelian and connected. The first result makes use of a generalized version of the analysis of bad groups.

In this paper, we shall survey results about the group-theoretic properties of stable groups. These can be classified into three main categories, according to the strength of the assumptions needed: chain conditions, generic types, and some form of rank. Each category has its typical application: Chain conditions often allow us to deduce global properties from local ones, generic properties are used to get definable groups from undefinable ones, and rank is necessary to interpret fields in certain group actions. While originally (...) the main input came from algebraic group theory, founded on the similarities between rank and dimension, increasingly methods borrowed from finite group theory have come to play a rôle, emphasizing the study of characteristic subgroups and characteristic families of subgroups. (shrink)

We prove that a stable solvable group G which satisfies xn = 1 generically is of finite exponent dividing some power of n. Furthermore, G is nilpotent-by-finite. A second result is that in a stable group of finite exponent, involutions either have big centralisers, or invert a subgroup of finite index (which hence has to be abelian).

We define a reasonably well-behaved class of ultraimaginaries, i.e. classes modulo [Formula: see text]-invariant equivalence relations, called tame, and establish some basic simplicity-theoretic facts. We also show feeble elimination of supersimple ultraimaginaries: If [Formula: see text] is an ultraimaginary definable over a tuple [Formula: see text] with [Formula: see text], then [Formula: see text] is eliminable up to rank [Formula: see text]. Finally, we prove some uniform versions of the weak canonical base property.

An infinite field with only countably many pure types is algebraically closed.

If * is a binary partial function which happens to be a group law on some infinite subset of some model of a stable theory, then this subset can be embedded into a definable group such that * becomes the group operation.

We show that a stable groupG satisfying certain commutator conditions is nilpotent. Furthermore, a soluble stable group with generically splitting automorphism of prime order is nilpotent-by-finite. In particular, a soluble stable group with a generic element of prime order is nilpotent-by-finite.

We shall define a general notion of dimension, and study groups and rings whose interpretable sets carry such a dimension. In particular, we deduce chain conditions for groups, definability results for fields and domains, and show that a pseudofinite $\widetilde {\mathfrak M}_c$ -group of finite positive dimension contains a finite-by-abelian subgroup of positive dimension, and a pseudofinite group of dimension 2 contains a soluble subgroup of dimension 2.

A review of fraud in medical research in Britain, Europe, the USA and Australia. It includes a history of known cases of fraud since 1974 and discusses ways for detecting and dealing with fraud that have been devised by government agencies, pharmaceutical companies, academic institutions and scientific publications (especially medical journals).

This article traces certain rhetorics of knowledge-change as well as a few models of such change. In particular, it focuses on models that emphasize novelty and sudden transformation. To this end, the works of Thomas Kuhn, and the debates surrounding his celebrated modeling of the paradigm, are explored. Having established – at least in an illustrative fashion – the role of novelty in Kuhn’s philosophy of science, we then look more briefly at the mid-career work of Michel Foucault (his Order (...) of Things and the Archaeology of Knowledge ), and the debate between Jürgen Habermas and Jean-François Lyotard to find (in Foucault’s case) analogies with the earlier models and debates surrounding Popper and Kuhn, and then (in the Habermas/Lyotard discussion), to see how revolutionary and reactionary status count in assigning value to models of knowledge. In all these inquiries, we seek less to criticize particular theorists (that has already been done) than to understand a dominant strand of understanding of knowledge and knowledge-change in the contemporary academy. (shrink)

Non-$n$-ampleness as defined by Pillay [20] and Evans [5] is preserved under analysability. Generalizing this to a more general notion of $\Sigma$-ampleness, this gives an immediate proof for all simple theories of a weakened version of the Canonical Base Property (CBP) proven by Chatzidakis [4] for types of finite SU-rank. This is then applied to the special case of groups.

If ${\mathfrak {F}}$ is a type-definable family of commensurable subsets, subgroups or subvector spaces in a metric structure, then there is an invariant subset, subgroup or subvector space commensurable with ${\mathfrak {F}}$. This in particular applies to type-definable or hyper-definable objects in a classical first-order structure.

An ω-categorical supersimple group is finite-by-abelian-by-finite, and has finite SU-rank. Every definable subgroup is commensurable with an acl( $\emptyset$ )-definable subgroup. Every finitely based regular type in a CM-trivial ω-categorical simple theory is non-orthogonal to a type of SU-rank 1. In particular, a supersimple ω-categorical CM-trivial theory has finite SU-rank.

America frequently talks about impeaching a president, but the impeachment provisions of the American constitution are widely misunderstood. In High Crimes and Misdemeanors, constitutional scholar Frank O. Bowman, III offers unprecedented clarity to the question of impeachment, tracing its roots to medieval England through its adoption in the Constitution and 250 years of American experience. By examining the human and political history of those who have faced impeachment, Bowman demonstrates that the Framers intended impeachment to be a flexible tool, (...) adaptable to the needs of any age. Written in a lively, engaging style, the book combines a deep historical and constitutional analysis of the impeachment clauses, a coherent theory of when impeachment should be used to protect constitutional order against presidential misconduct, and a comprehensive presentation of the case for and against impeachment of President Trump. It is an indispensable work for the present moment. (shrink)

We reconstruct the group action in the group configuration theorem. We apply it to show that in an ω-categorical theory a finitely based pseudolinear regular type is locally modular, and the geometry associated to a finitely based locally modular regular type is projective geometry over a finite field.

A totally ordered group G is essentially periodic if for every definable non-trivial convex subgroup H of G every definable subset of G is equal to a finite union of cosets of subgroups of G on some interval containing an end segment of H; it is coset-minimal if all definable subsets are equal to a finite union of cosets, intersected with intervals. We study definable sets and functions in such groups, and relate them to the quasi-o-minimal groups introduced in Belegradek (...) et al. . Main results: An essentially periodic group G is abelian; if G is discrete, then definable functions in one variable are ultimately piecewise linear. A group such that every model elementarily equivalent to it is coset-minimal is quasi-o-minimal , and its definable functions in one variable are piecewise linear. (shrink)

We study local strengthenings of the simplicity condition. In particular, we define and study a local Lascar rank, as well as short, low, supershort and superlow theories. An example of a low, non supershort theory is given.

1. We show that if p is a real type which is internal in a set $\sigma$ of partial types in a simple theory, then there is a type p' interbounded with p, which is finitely generated over $\sigma$ , and possesses a fundamental system of solutions relative to $\sigma$ . 2. If p is a possibly hyperimaginary Lascar strong type, almost \sigma-internal$ , but almost orthogonal to $\sigma^{\omega}$ , then there is a canonical non-trivial almost hyperdefinable polygroup which multi-acts (...) on p while fixing $\sigma$ generically. In case p is $\sigma-internal$ and T is stable, this is the binding group of p over \sigma$. (shrink)

If G is an omega-stable group with a normal definable subgroup H, then the Sylow-2-subgroups of G/H are the images of the Sylow-2-subgroups of G. /// Sei G eine omega-stabile Gruppe und H ein definierbarer Normalteiler von G. Dann sind die Sylow-2-Untergruppen von G/H Bilder der Sylow-2-Untergruppen von G.

We show that if p is a real type which is almost internal in a formula φ in a simple theory, then there is a type p' interalgebraic with a finite tuple of realizations of p, which is generated over φ. Moreover, the group of elementary permutations of p' over all realizations of φ is type-definable.