On computable automorphisms of the rational numbers

2001 ◽  
Vol 66 (3) ◽  
pp. 1458-1470 ◽  
Author(s):  
A. S. Morozov ◽  
J. K. Truss
Keyword(s):  
Rational Numbers ◽  
Isomorphism Type ◽  
Turing Degrees ◽  
First Order ◽  
Principal Ideals ◽  
General Correspondence ◽  
The Relationship ◽  
The Ideal

AbstractThe relationship between ideals I of Turing degrees and groups of I-recursive automorphisms of the ordering on rationals is studied. We discuss the differences between such groups and the group of all automorphisms, prove that the isomorphism type of such a group completely defines the ideal I, and outline a general correspondence between principal ideals of Turing degrees and the first-order properties of such groups.

Recursive isomorphism types of recursive Boolean algebras

1981 ◽  
Vol 46 (3) ◽  
pp. 572-594 ◽  
Author(s):  
J. B. Remmel
Keyword(s):  
Boolean Algebra ◽  
Recursive Function ◽  
Boolean Algebras ◽  
Isomorphism Type ◽  
Turing Degrees ◽  
Main Question ◽  
Partial Recursive Function ◽  
Recursive Isomorphism ◽  
Infinite Set ◽  
The Ideal

A Boolean algebra is recursive if B is a recursive subset of the natural numbers N and the operations ∧ (meet), ∨ (join), and ¬ (complement) are partial recursive. Given two Boolean algebras and , we write if is isomorphic to and if is recursively isomorphic to , that is, if there is a partial recursive function f: B1 → B2 which is an isomorphism from to . will denote the set of atoms of and () will denote the ideal generated by the atoms of .One of the main questions which motivated this paper is “To what extent does the classical isomorphism type of a recursive Boolean algebra restrict the possible recursion theoretic properties of ?” For example, it is easy to see that must be co-r.e. (i.e., N − is an r.e. set), but can be immune, not immune, cohesive, etc? It follows from a result of Goncharov [4] that there exist classical isomorphism types which contain recursive Boolean algebras but do not contain any recursive Boolean algebras such that is recursive. Thus the classical isomorphism can restrict the possible Turing degrees of , but what is the extent of this restriction? Another main question is “What is the recursion theoretic relationship between and () in a recursive Boolean algebra?” In our attempt to answer these questions, we were led to a wide variety of recursive isomorphism types which are contained in the classical isomorphism type of any recursive Boolean algebra with an infinite set of atoms.

PROPAGATING COVARIANCE IN COMPUTER VISION

1996 ◽  
Vol 10 (05) ◽  
pp. 561-572 ◽  
Author(s):  
ROBERT M. HARALICK
Keyword(s):  
Random Perturbation ◽  
Taylor Series Expansion ◽  
Random Perturbations ◽  
Input Quantity ◽  
First Order ◽  
Statistical Behavior ◽  
Vision Algorithm ◽  
The Relationship ◽  
Output Quantity ◽  
The Ideal

This paper describes how to propagate approximately additive random perturbations through any kind of vision algorithm step in which the appropriate random perturbation model for the estimated quantity produced by the vision step is also an additive random perturbation. We assume that the vision algorithm step can be modeled as a calculation (linear or non-linear) that produces an estimate that minimizes an implicit scaler function of the input quantity and the calculated estimate. The only assumption is that the scaler function has finite second partial derivatives and that the random perturbations are small enough so that the relationship between the scaler function evaluated at the ideal but unknown input and output quantities and the observed input quantity and perturbed output quantity can be approximated sufficiently well by a first order Taylor series expansion. The paper finally discusses the issues of verifying that the derived statistical behavior agrees with the experimentally observed statistical behavior.

Nonlinear Analysis of Visual Evoked Potentials Elicited by Color Stimulation

1997 ◽  
Vol 36 (04/05) ◽  
pp. 315-318 ◽  
Author(s):  
K. Momose ◽  
K. Komiya ◽  
A. Uchiyama
Keyword(s):  
Visual System ◽  
Evoked Potentials ◽  
Visual Evoked Potentials ◽  
Normal Subjects ◽  
Second Order ◽  
First Order ◽  
The Relationship ◽  
Perceived Color ◽  
Second Order Nonlinearity ◽  
Visual Evoked

Abstract:The relationship between chromatically modulated stimuli and visual evoked potentials (VEPs) was considered. VEPs of normal subjects elicited by chromatically modulated stimuli were measured under several color adaptations, and their binary kernels were estimated. Up to the second-order, binary kernels obtained from VEPs were so characteristic that the VEP-chromatic modulation system showed second-order nonlinearity. First-order binary kernels depended on the color of the stimulus and adaptation, whereas second-order kernels showed almost no difference. This result indicates that the waveforms of first-order binary kernels reflect perceived color (hue). This supports the suggestion that kernels of VEPs include color responses, and could be used as a probe with which to examine the color visual system.

KONSTRUKSI ISLAM DALAM KEKUASAAN NEGARA

1970 ◽  
Vol 6 (2) ◽  
Author(s):  
Nurul Aini Musyarofah
Keyword(s):  
Islamic Law ◽  
Social Condition ◽  
The Other ◽  
Good Society ◽  
Ideal Form ◽  
Other Hand ◽  
Islamic Politics ◽  
The Relationship ◽  
The Ideal

The relationship between Islam and state raises a controversy that includes two main groups;formalists and substantialists. Both of them intend to achieve a good social condition which is inaccordance with Islamic politics. The ideal form of good society to be achieved is principallydescribed in the main source of Islamic law, Al Qur’an and As Sunnah, as follows. A form of goodsociety should supprot equality and justice, egalitarianism, and democracy in its social community.The next problem is what the needed methods and instruments to achieve the ideal Islamic politicsare. In this case, the debate on the formalization and substance of Islamic teaching is related to therunning formal political institution.Each group claims itself to be the most representative to the ideal Islam that often leads to anescalating conflict. On the other hand thr arguments of both groups does not reach the wholeMuslims. As a result, the discourse of Islam and state seems to be elitist and political. As a result,Both groups suspect each other each other and try to utilize the controversy on the relationshipbetween Islam and state to get their own benefit which has no relation with the actualization ofIslamic teaching.

Esteem and self-esteem as an interweaving polarity. Max Weber´s analysis from the Protestant ethic to the ideal-type of politician

Human Affairs ◽  
2020 ◽  
Vol 30 (3) ◽  
pp. 353-364
Author(s):  
Cristiana Senigaglia
Keyword(s):  
Social Life ◽  
Max Weber ◽  
Modern Society ◽  
Self Esteem ◽  
Protestant Ethic ◽  
Social Reputation ◽  
Conduct Of Life ◽  
The Social ◽  
The Relationship ◽  
The Ideal

AbstractAlthough Max Weber does not specifically analyze the topic of esteem, his investigation of the Protestant ethic offers interesting insights into it. The change in mentality it engendered essentially contributed to enhancing the meaning and importance of esteem in modern society. In his analysis, Weber ascertains that esteem was fundamental to being accepted and integrated into the social life of congregations. Nevertheless, he also highlights that esteem was supported by a form of self-esteem which was not simply derived from a good social reputation, but also achieved through a deep and continual self-analysis as well as a strict discipline in the ethical conduct of life. The present analysis reconstructs the different aspects of the relationship between social and self-esteem and analyzes the consequences of that relationship by focusing on the exemplary case of the politician’s personality and ethic.

scholarly journals On the correspondence between nested calculi and semantic systems for intuitionistic logics

2020 ◽  
Author(s):  
Tim Lyon
Keyword(s):  
Intuitionistic Logic ◽  
Structural Rules ◽  
First Order ◽  
Constant Domains ◽  
The Relationship ◽  
Intuitionistic Logics

Abstract This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is shown that Fitting’s nested calculi naturally arise from their corresponding labelled calculi—for each of the aforementioned logics—via the elimination of structural rules in labelled derivations. The translational correspondence between the two types of systems is leveraged to show that the nested calculi inherit proof-theoretic properties from their associated labelled calculi, such as completeness, invertibility of rules and cut admissibility. Since labelled calculi are easily obtained via a logic’s semantics, the method presented in this paper can be seen as one whereby refined versions of labelled calculi (containing nested calculi as fragments) with favourable properties are derived directly from a logic’s semantics.

Relational Chase Procedures Interpreted as Resolution with Paramodulation1

1991 ◽  
Vol 15 (2) ◽  
pp. 123-138
Author(s):  
Joachim Biskup ◽  
Bernhard Convent
Keyword(s):  
Alternative Interpretation ◽  
Order Logic ◽  
First Order Logic ◽  
Inference Problem ◽  
First Order ◽  
Inference Problems ◽  
The One ◽  
The Relationship ◽  
Theoretical Foundations ◽  
Insight Into

In this paper the relationship between dependency theory and first-order logic is explored in order to show how relational chase procedures (i.e., algorithms to decide inference problems for dependencies) can be interpreted as clever implementations of well known refutation procedures of first-order logic with resolution and paramodulation. On the one hand this alternative interpretation provides a deeper insight into the theoretical foundations of chase procedures, whereas on the other hand it makes available an already well established theory with a great amount of known results and techniques to be used for further investigations of the inference problem for dependencies. Our presentation is a detailed and careful elaboration of an idea formerly outlined by Grant and Jacobs which up to now seems to be disregarded by the database community although it definitely deserves more attention.

scholarly journals A question of van den Dries and a theorem of Lipshitz and Robinson; Not everything is standard

2007 ◽  
Vol 72 (1) ◽  
pp. 119-122 ◽  
Author(s):  
Ehud Hrushovski ◽  
Ya'acov Peterzil
Keyword(s):  
Real Numbers ◽  
The Real ◽  
First Order ◽  
Real Closed Fields ◽  
Minimal Structure ◽  
Closed Fields ◽  
New Construction ◽  
The Relationship

AbstractWe use a new construction of an o-minimal structure, due to Lipshitz and Robinson, to answer a question of van den Dries regarding the relationship between arbitrary o-minimal expansions of real closed fields and structures over the real numbers. We write a first order sentence which is true in the Lipshitz-Robinson structure but fails in any possible interpretation over the field of real numbers.

Joseph Soloveitchik and Immanuel Kant's Mitzvah-Aesthetic

AJS Review ◽  
2001 ◽  
Vol 25 (1) ◽  
pp. 1-24 ◽  
Author(s):  
Zachary Braiterman
Keyword(s):  
Immanuel Kant ◽  
Social Ethics ◽  
Formal System ◽  
Order Effects ◽  
Critique Of Judgment ◽  
Jewish Thought ◽  
Personal Morality ◽  
History Of ◽  
The Relationship ◽  
The Ideal

In the following pages, I will address the relationship between Jewish thought and aesthetics by bringing Joseph Soloveitchik into conversation with Immanuel Kant, whose Critique of Judgment remains an imposing monument in the history of philosophical aesthetics. While Buber and Rosenzweig may have been more accomplished aesthetes, Soloveitchik's aesthetic proves closer to Kant's own. In particular, I draw upon the latter's distinction between the beautiful and the sublime and the notion of a form of indeterminate purposiveness without determinate purpose. I will relate these three figures to Soloveitcchik's understanding of halakhah and to the ideal of performing commandments for their own sake (li-shemah). The model of mitzvah advanced by this comparison is quintessentially modern: an autonomous, self-contained, formal system that does not (immediately) point to extraneous goods, such as spiritual enlightenment, personal morality, or social ethics. The good presupposed by this system proves first and foremost “aesthetic.” That is, immanent to the system. Supererogatory goods enter into the picture only afterward as second-order effects.

scholarly journals THE n-r.e. DEGREES: UNDECIDABILITY AND Σ1 SUBSTRUCTURES

2012 ◽  
Vol 12 (01) ◽  
pp. 1250005 ◽  
Author(s):  
MINGZHONG CAI ◽  
RICHARD A. SHORE ◽  
THEODORE A. SLAMAN
Keyword(s):  
Turing Degrees ◽  
First Order ◽  
Global Properties

We study the global properties of [Formula: see text], the Turing degrees of the n-r.e. sets. In Theorem 1.5, we show that the first order of [Formula: see text] is not decidable. In Theorem 1.6, we show that for any two n and m with n < m, [Formula: see text] is not a Σ1-substructure of [Formula: see text].

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