In this article we find some sufficient and some necessary ${\Sigma^1_1}$ -conditions with oracles for a model to be resplendent or chronically resplendent. The main tool of our proofs is internal arguments, that is analogues of classical theorems and model-theoretic constructions conducted inside a model of first-order Peano Arithmetic: arithmetised back-and-forth constructions and versions of the arithmetised completeness theorem, namely constructions of recursively saturated and resplendent models from the point of view of a model of arithmetic. (...) These internal arguments are used in conjunction with Pabion’s theorem that ensures that certain oracles are coded in a sufficiently saturated model of arithmetic. Examples of applications are provided for the theories of dense linear orders and of discrete linear orders. These results are then generalised to other ω-categorical theories and theories with a unique countable recursively saturated model. (shrink)

In this paper we show that in every |T |+-resplendent model N , for every A ⊆ N such that |A | ≤ |T |, the group Autf of strong automorphisms is the least very normal subgroup of the group Aut and the quotient Aut/Autf is the Lascar group over A . Then we generalize this result to every |T |+-saturated and strongly |T |+-homogeneous model.

In this article we find some sufficient and some necessary \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma^1_1}$$\end{document} -conditions with oracles for a model to be resplendent or chronically resplendent. The main tool of our proofs is internal arguments, that is analogues of classical theorems and model-theoretic constructions conducted inside a model of first-order Peano Arithmetic: arithmetised back-and-forth constructions and versions of the arithmetised completeness theorem, namely constructions of recursively saturated and resplendent models from (...) the point of view of a model of arithmetic. These internal arguments are used in conjunction with Pabion’s theorem that ensures that certain oracles are coded in a sufficiently saturated model of arithmetic. Examples of applications are provided for the theories of dense linear orders and of discrete linear orders. These results are then generalised to other ω-categorical theories and theories with a unique countable recursively saturated model. (shrink)

In this article we find some sufficient and some necessary \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma^1_1}$$\end{document} -conditions with oracles for a model to be resplendent or chronically resplendent. The main tool of our proofs is internal arguments, that is analogues of classical theorems and model-theoretic constructions conducted inside a model of first-order Peano Arithmetic: arithmetised back-and-forth constructions and versions of the arithmetised completeness theorem, namely constructions of recursively saturated and resplendent models from (...) the point of view of a model of arithmetic. These internal arguments are used in conjunction with Pabion’s theorem that ensures that certain oracles are coded in a sufficiently saturated model of arithmetic. Examples of applications are provided for the theories of dense linear orders and of discrete linear orders. These results are then generalised to other ω-categorical theories and theories with a unique countable recursively saturated model. (shrink)

Let T be a complete countable first order theory and λ an uncountable cardinal. Theorem 1. If T is not superstable, T has 2 λ resplendent models of power λ. Theorem 2. If T is strictly superstable, then T has at least $\min(2^\lambda,\beth_2)$ resplendent models of power λ. Theorem 3. If T is not superstable or is small and strictly superstable, then every resplendent homogeneous model of T is saturated. Theorem 4 (with Knight). For each (...) μ ∈ ω ∪ {ω, 2 ω } there is a recursive theory in a finite language which has μ resplendent models of power κ for every infinite κ. (shrink)

We expand the notion of resplendency to theories of the kind T + p", where T is a fi rst-order theory and p" expresses that the type p is omitted. We investigate two di erent formulations and prove necessary and sucient conditions for countable recursively saturated models of PA. Some of the results in this paper can be found in one of the author's doctoral thesis [3].

We prove results about nonstandard formulas in models of Peano arithmetic which complement those of Kotlarski, Krajewski, and Lachlan in [KKL] and [L]. This enables us to characterize both recursive saturation and resplendency in terms of statements about nonstandard sentences. Specifically, a model M of PA is recursively saturated iff M is nonstandard and M-logic is consistent.M is resplendent iff M is nonstandard, M-logic is consistent, and every sentence φ which is consistent in M-logic is contained in a (...) full satisfaction class for M. Thus, for models of PA, recursive saturation can be expressed by a (standard) Σ 1 1 -sentence and resplendency by a ▵ 1 2 -sentence. (shrink)

Kreisel’s set-theoretic problem is the problem as to whether any logical consequence of ZFC is ensured to be true. Kreisel and Boolos both proposed an answer, taking truth to mean truth in the background set-theoretic universe. This article advocates another answer, which lies at the level of models of set theory, so that truth remains the usual semantic notion. The article is divided into three parts. It first analyzes Kreisel’s set-theoretic problem and proposes one way in which any model (...) of set theory can be compared to a background universe and shown to contain internal models. It then defines logical consequence with respect to a model of ZFC, solves the model-scaled version of Kreisel’s set-theoretic problem, and presents various further results bearing on internal models. Finally, internal models are presented as accessible worlds, leading to an internal modal logic in which internal reflection corresponds to modal reflexivity, and resplendency corresponds to modal axiom 4. (shrink)

We prove that every relation-universal model of an ω-stable theory is saturated. We also show there is a large class of ω-stable theories for which every resplendent model is homogeneous.

" In Imagination and the Meaningful Brain, psychoanalyst Arnold Modell claims that subjective human experience must be included in any scientific...

Abstract.Since the gene splicing debates of the 1980s, the public has been exposed to an ongoing sequence of genetic and reproductive technologies. Many issue areas have outcomes that lose track of people's inner values or engender opposing religious viewpoints defying final resolution. This essay relocates the discussion of what is an acceptable application from the individual to the societal level, examining technologies that stand to address large numbers of people and thus call for policy resolution, rather than individual fiat, in (...) their application. A major source of guidance is the “Genetic Frontiers” series of professional dialogues and conferences held by the National Conference for Community and Justice from 2002 to 2004. Genetic testing, human gene therapy, genetic engineering of plants and animals, and stem cell technology are examined. While differences in perspective on the beginning of life persist, a stepwise approach to the examination of genetic testing reveals areas of general agreement. Stewardship of life, human co‐creativity with the divine, and social justice help define the bounds of application of genetic engineering and therapy; compassionate care plays a major role in establishing stem cell policy. Active, sustained dialogue is a useful resource for enabling sharing of religious values and crystallization of policies. (shrink)

Aristotle is oftentimes viewed through a strictly philosophical lens as heir to Plato and has having introduced logical rigor where an emphasis on the theory of Forms formerly prevailed. It must be appreciated that Aristotle was the son of a physician, and that his inculcation of the thought of other Greek philosophers addressing health and the natural elements led to an extremely broad set of biologically- and medically-related writings. As this article proposes, Aristotle deepened the fourfold theory of the elements (...) with anatomic and physiologic observations. In books like History of Animals, Parts of Animals, and the lost Anatomai, he actively dissected organisms and recorded his findings. The corpus of medically-related literature Aristotle developed had a direct influence on subsequent Greek thinkers, including Galen, and on Medieval Islamic and modern Western practitioners such as William Harvey. Aristotle's ideas continue to influence modern medical thinkers in Europe and America through both his interpretation by European philosophers gaining the attention of medical humanists, and his writings' enduring impact on medical researchers balancing scientific with more personalistic approaches to medicine. (shrink)

The estrangement between genetic scientists and theologians originating in the 1960s is reflected in novel combinations of human thought (subject) and genes (investigational object), paralleling each other through the universal process known in chaos theory as self-similarity. The clash and recombination of genes and knowledge captures what Philip Hefner refers to as irony, one of four voices he suggests transmit the knowledge and arguments of the religion-and-science debate. When viewed along a tangent connecting irony to leadership, journal dissemination, and the (...) activities of the "public intellectual" and the public at large, the sequence of voices is shown to resemble the passage of genetic information from DNA to mRNA, tRNA, and protein, and from cell nucleus to surrounding environment. In this light, Hefner's inquiry into the voices of Zygon is bound up with the very subject matter Zygon covers. (shrink)