Recursive well-orderings

1955 ◽  
Vol 20 (2) ◽  
pp. 151-163 ◽  
Author(s):  
Clifford Spector
Keyword(s):  
Ordinal Number ◽  
Decision Problems ◽  
Natural Numbers ◽  
Mathematical Objects ◽  
Hyperarithmetical Hierarchy ◽  
Ordinal Notations ◽  
The One ◽  
The Church ◽  
Number Class

Cantor's second ordinal number class is perhaps the simplest example of a set of mathematical objects which cannot all be named in one language. In this paper we shall investigate a system of names for a segment of the first and second number classes in relation to decision problems. The system, except for one minor difference, is the one studied by Markwald in [12]. In our system ordinals are named by natural numbers from a set W via recursive well-orderings of subsets of the natural numbers.The decision problems will be related to the hyperarithmetical hierarchy of Davis [2], [3] and Kleene [8]. This hierarchy is indexed by ordinal notations from Kleene's system S3 [4], [6], [9], in which ordinals are named by natural numbers from a set O, partially well-ordered ([12] p. 138) by a relation a≤Ob; O and ≤O are defined inductively by applications of the successor and limit operations. As results of this investigation, we shall (i) answer negatively Markwald's question [12] Theorem 12 whether his set “W” is arithmetical by showing that it is not even hyperarithmetical, (ii) obtain a new proof of the main result of Kleene [10] that every predicate expressible in both the one-function-quantifier forms of [8] is recursive in Hα for some aεO, (iii) answer affirmatively the question raised by Davis [2], [3] whether all the Church-Kleene constructive ordinals are uniqueness ordinals, and (iv) solve the function-quantifier analog of Post's problem [15]. Strong use will be made of the well-orderings that can be constructed from one-function-quantifier predicates as in [9].

Christus Virgo

2012 ◽  
Vol 41 (2) ◽  
pp. 22-27
Author(s):  
Sissel Undheim
Keyword(s):  
Moral Status ◽  
The Other ◽  
Late Antique ◽  
Church Fathers ◽  
Early Christian ◽  
Female Sex ◽  
The One ◽  
The Church

The description of Christ as a virgin, 'Christus virgo', does occur at rare occasions in Early Christian and late antique texts. Considering that 'virgo' was a term that most commonly described the sexual and moral status of a member of the female sex, such representations of Christ as a virgin may exemplify some of the complex negotiations over gender, salvation, sanctity and Christology that we find in the writings of the Church fathers. The article provides some suggestions as to how we can understand the notion of the virgin Christ within the context of early Christian and late antique theological debates on the one hand, and in light of the growing interest in sacred virginity on the other.

Solidaritas Sebagai Norma Dasar Dalam Etika Paulus

1970 ◽  
Vol 11 (1) ◽  
pp. 79-100
Author(s):  
Martin Harun
Keyword(s):  
Community Building ◽  
Lord's Supper ◽  
Body Of Christ ◽  
The Poor ◽  
Central Elements ◽  
The New Testament ◽  
Unity In Diversity ◽  
The One ◽  
The Church ◽  
Different Parts

Abstract: Solidarity, a modern word and concept, has old roots in the concept of koinonia (fellowship) as it is understood in the New Testament. David G. Horrell even maintains that what we now call solidarity, functions as a meta norm in Paul’s ethics, since phenomena of solidarity are clearly present in the central elements of Paul’s community building. Reference is made to the two basic rituals, Baptism and the Lord’s Supper, which build unity in diversity; to the most frequently used form of address, adelphoi/brothers, which asks for familial treatment of one another; also to the special way in which Paul often tries to restore unity in the middle of conflicts; and especially to his metaphor of the Church as the one body of Christ with many different parts that need and support one another. When speaking about the collections as a sign of the Greek community’s solidarity with the poor community in Jerusalem, Paul refers to Christ’s solidarity as the source of solidarity within and among communities. Keywords: Solidarity, fellowship, David Horrell, Paul, Ethics, baptism, the Lord’s Supper, brothers, Body of Christ, Christ’s solidarity. Abstrak: Solidaritas, sebuah kata dan paham modern, memiliki akar yang lama, antara lain dalam paham koinonia (persekutuan), sebagaimana digunakan dalam Alkitab Perjanjian Baru. David G. Horrell mempertahankan bahwa apa yang sekarang kita sebut solidaritas, merupakan norma dasar (meta norm) dalam etika Paulus, sebab fenomen-fenomen solidaritas tampak dalam unsur-unsur sentral pembinaan jemaatnya, antara lain dalam kedua ritual paling dasar, baptisan dan perjamuan Tuhan, yang membina kesatuan dalam perbedaan. Solidaritas juga muncul dalam sebutan paling frekuen, saudara-saudara (adelphoi), yang menuntut suatu etos kekeluargaan. Solidaritas juga tampak dalam banyak seruan Paulus untuk memulihkan kesatuan apabila ia berhadapan dengan perpecahan, dan teristimewa dalam menggambarkan jemaat sebagai satu tubuh Kristus dengan banyak anggota yang berbeda dan saling membutuhkan serta memberi. Dalam konteks kolekte-kolekte sebagai tanda solidaritas antarjemaat, Paulus secara eksplisit menunjuk kepada solidaritas Kristus dengan kita sebagai dasar terdalam dari solidaritas antarumat. Kata-kata kunci: Solidaritas, persekutuan, David Horrell, Paulus, etika, baptisan, Perjamuan Tuhan, saudara-saudara, Tubuh Kristus, solidaritas Kristus.

The Invention of Papal History

2019 ◽  
Author(s):  
Stefan Bauer
Keyword(s):  
Catholic Reformation ◽  
History Writing ◽  
Historical Texts ◽  
The Past ◽  
History Of ◽  
Cultural Standards ◽  
Commissioned Works ◽  
The One ◽  
Late Renaissance ◽  
The Church

How was the history of post-classical Rome and of the Church written in the Catholic Reformation? Historical texts composed in Rome at this time have been considered secondary to the city’s significance for the history of art. The Invention of Papal History corrects this distorting emphasis and shows how history-writing became part of a comprehensive formation of the image and self-perception of the papacy. By presenting and fully contextualizing the path-breaking works of the Augustinian historian Onofrio Panvinio (1530–68), this book shows what type of historical research was possible in the late Renaissance and the Catholic Reformation. Historiography in this period by no means consisted entirely of commissioned works written for patrons; rather, a creative interplay existed between, on the one hand, the endeavours of authors to explore the past and, on the other hand, the constraints of patronage and ideology placed on them. This book sheds new light on the changing priorities, mentalities, and cultural standards that flourished in the transition from the Renaissance to the Catholic Reformation.

The Church of the Center

1997 ◽  
Vol 51 (2) ◽  
pp. 130-142
Author(s):  
Gabriel Fackre
Keyword(s):  
The One ◽  
The Church

Within contemporary Protestantism a center is emerging that is both evangelical and ecumenical. Its theology is controlled by neither cultural orthodoxies nor ideological wars; its loyalty is to Christ alone, the one center of the church.

The Political Theory of the Disruption

1916 ◽  
Vol 10 (3) ◽  
pp. 437-464 ◽  
Author(s):  
Harold J. Laski
Keyword(s):  
Political Theory ◽  
Political Authority ◽  
The State ◽  
The Political ◽  
The Reformation ◽  
Secular Society ◽  
The One ◽  
Definition Of ◽  
Political Principles ◽  
The Church

“Of political principles,” says a distinguished authority, “whether they be those of order or of freedom, we must seek in religious and quasi-theological writings for the highest and most notable expressions.” No one, in truth, will deny the accuracy of this claim for those ages before the Reformation transferred the centre of political authority from church to state. What is too rarely realised is the modernism of those writings in all save form. Just as the medieval state had to fight hard for relief from ecclesiastical trammels, so does its modern exclusiveness throw the burden of a kindred struggle upon its erstwhile rival. The church, intelligibly enough, is compelled to seek the protection of its liberties lest it become no more than the religious department of an otherwise secular society. The main problem, in fact, for the political theorist is still that which lies at the root of medieval conflict. What is the definition of sovereignty? Shall the nature and personality of those groups of which the state is so formidably one be regarded as in its gift to define? Can the state tolerate alongside itself churches which avow themselves societates perfectae, claiming exemption from its jurisdiction even when, as often enough, they traverse the field over which it ploughs? Is the state but one of many, or are those many but parts of itself, the one?

ON THE DENSITY OF HAUSDORFF DIMENSIONS OF BOUNDED TYPE CONTINUED FRACTION SETS: THE TEXAN CONJECTURE

2004 ◽  
Vol 04 (01) ◽  
pp. 63-76 ◽  
Author(s):  
OLIVER JENKINSON
Keyword(s):  
Hausdorff Dimension ◽  
Finite Subset ◽  
Continued Fraction ◽  
Cantor Set ◽  
Computational Method ◽  
Accurate Approximation ◽  
Natural Numbers ◽  
Important Special Case ◽  
The One ◽  
Special Case

Given a non-empty finite subset A of the natural numbers, let EA denote the set of irrationals x∈[0,1] whose continued fraction digits lie in A. In general, EA is a Cantor set whose Hausdorff dimension dim (EA) is between 0 and 1. It is shown that the set [Formula: see text] intersects [0,1/2] densely. We then describe a method for accurately computing dimensions dim (EA), and employ it to investigate numerically the way in which [Formula: see text] intersects [1/2,1]. These computations tend to support the conjecture, first formulated independently by Hensley, and by Mauldin & Urbański, that [Formula: see text] is dense in [0,1]. In the important special case A={1,2}, we use our computational method to give an accurate approximation of dim (E{1,2}), improving on the one given in [18].

‘A Moment of Truth’? The Church and Political Change in Malawi, 1992

1995 ◽  
Vol 33 (2) ◽  
pp. 243-262 ◽  
Author(s):  
Jonathan Newell
Keyword(s):  
Catholic Church ◽  
Party System ◽  
Urban Riots ◽  
Congress Party ◽  
Industrial Action ◽  
Political Dominance ◽  
Entire Nation ◽  
The One ◽  
Democratic Elections ◽  
The Church

The immediate origins of the democratic elections held in Malawi in 1994, which brought to an end over 30 years of political dominance by President Kamuzu Banda and the Malawi Congress Party (MCP), lie in the unprecedented events which shook the entire nation in 1992. Although that turbulent year was characterised by industrial action, serious urban riots, student demonstrations, the emergence of new domestic political groupings, and the Government's agreement to hold a national referendum on the future of the one-party system in the country, in retrospect perhaps what was most remarkable about these developments was that they were sparked off by the Catholic Church, and that their momentum was sustained at crucial stages by other Christian denominations in Malawi.1

The Christian Church in the Last Seventy Years

1943 ◽  
Vol 12 (1) ◽  
pp. 28-34
Author(s):  
Kenneth Scott Latourette
Keyword(s):  
Large Volume ◽  
The Other ◽  
Recent History ◽  
Christian Church ◽  
The Past ◽  
Other Hand ◽  
The Status ◽  
The One ◽  
The Church

A strange contrast exists in the status of the Christian Church in the past seventy years. On the one hand the Church has clearly lost some of the ground which once appeared to be safely within its possession. On the other hand it has become more widely spread geographically and, when all mankind is taken into consideration, more influential in shaping human affairs than ever before in its history. In a paper as brief as this must of necessity be, space can be had only for the sketching of the broad outlines of this paradox and for suggesting a reason for it. If details were to be given, a large volume would be required. Perhaps, however, we can hope to do enough to point out one of the most provocative and important set of movements in recent history.

scholarly journals Onherhaalbaar, onontdoenbaar: Die doop as simbool van eenheid in die kerk

2013 ◽  
Vol 69 (1) ◽  
Author(s):  
David A. Van Oudtshoorn
Keyword(s):  
Pastoral Care ◽  
Later Life ◽  
Phenomenological Analysis ◽  
Theological Reflection ◽  
Spiritual Journey ◽  
Spiritual Experiences ◽  
The One ◽  
Expanded Concept ◽  
The Church ◽  
Significant Milestone

Irrevocably singular: Baptism as a symbol of unity in the church. In this article I conduct a phenomenological analysis of the concept ‘one baptism’ in Ephesians 4:4−6. Such an analysis seeks to reveal the essence of a particular concept by bracketing out the theological and ideological presuppositions usually associated with it. The essential concept is then expanded by linking it to the terms most closely surrounding it in the text. A critical theological reflection on the expanded concept shows that ‘one baptism’ refers to an event by which believers are inducted, once and for all, into the church as the one body of the one Lord, Jesus Christ. The church exists through the presence of the one Spirit who binds believers in an unbreakable bond of love to God and to each other. Because baptism can never be undone or repeated, any liturgical act depicted as a ‘re-baptism’ is, by definition, impossible. This means that churches that baptise the children of believing parents are able to accommodate requests from people who, having been baptised as an infant, in later life wish to celebrate and testify to some significant milestone in their spiritual journey by means of an official church ritual. Such ritualised testimonies, however, refer to the existential lifeworld of believers (their repentance, confession of faith etc.) and are distinct from baptism that refers to the singular eschatological work of Christ and thus cannot be repeated. The church should, however, take pastoral care to ensure that people do not substitute their own spiritual experiences for the reality of salvation that is founded on the singular act of God, for us once and for all in Christ, to which baptism irrevocably refers.

Charismata: Gifts, Enablements, or Ministries?

2002 ◽  
Vol 11 (1) ◽  
pp. 53-69
Author(s):  
Benny Aker
Keyword(s):  
New Testament ◽  
Spiritual Gifts ◽  
Biblical Theology ◽  
Church Culture ◽  
The New Testament ◽  
The One ◽  
The Church

AbstractIn the midst of a growing awareness of spiritual gifts in contemporary church culture and in the academy, much confusion exists. The use of the term 'charismata' promotes this confusion and is not an appropriate label for the biblical evidence of such activity. The problem lies in a deficient linguistic and exegetical handling of this term—a problem identified by James Barr long ago and brought to the fore by Kenneth Berding. Proper exegesis overcomes this prevalent exegetical and linguistic fallacy and suggests another term, diakonia. However, a more foundational conception of both the church and ministry is lacking. By analyzing Pauline anthropol ogy in Romans, an enduring and foundational model for gifts and ministries emerges. This model is the Pauline conception of the church as God's tem ple. People who are delivered from sin's power through identifying with Jesus' death, burial, and resurrection and who have the Spirit are free to give themselves both as sacrifice and temple servants in spiritual ministries. One other caution is raised and discussed. One must avoid the charge in practice and theology of Spirit-monism. Basic structures of the New Testament always place Jesus as the One through whom the Spirit comes. Conse quently, all Spirit activity must in some way be christological and sote riological in nature. Some contemporary applications are derived from this biblical theology of Church and ministry.

Sign in / Sign up

Export Citation Format

Share Document