scholarly journals Things that can and things that can’t be done in PRA

1998 ◽  
Vol 5 (18) ◽  
Author(s):  
Ulrich Kohlenbach
Keyword(s):  
Mathematical Reasoning ◽  
The Other ◽  
Function Parameter ◽  
Recursive Functions ◽  
Other Hand ◽  
Elementary Analysis ◽  
Primitive Recursive Arithmetic ◽  
Primitive Recursive ◽  
Different Levels ◽  
Bounded Sequences

It is well-known by now that large parts of (non-constructive) mathematical reasoning can be carried out in systems T which are conservative over primitive recursive arithmetic PRA (and even much weaker systems). On the other hand there are principles S of elementary analysis (like the Bolzano-Weierstrass principle, the existence of a limit superior for bounded sequences etc.) which are known to be equivalent to arithmetical<br />comprehension (relative to T ) and therefore go far beyond the strength of PRA (when added to T ). <br />In this paper we determine precisely the arithmetical and computational strength (in terms of optimal conservation results and subrecursive characterizations of provably recursive functions) of weaker function parameter-free schematic versions S− of S, thereby<br />exhibiting different levels of strength between these principles as well as a sharp borderline between fragments of analysis which are still conservative over PRA and extensions which just go beyond the strength of PRA.

A result on implications of Σ1-sentences and its application to normal form theorems

1981 ◽  
Vol 46 (3) ◽  
pp. 634-642
Author(s):  
Jean-Yves Girard ◽  
Peter Päppinghaus
Keyword(s):  
Normal Form ◽  
Reflection Principle ◽  
The Other ◽  
Other Hand ◽  
Primitive Recursive Arithmetic ◽  
Incompleteness Theorems ◽  
False Premise ◽  
Primitive Recursive ◽  
Gödel’S Incompleteness Theorems

In this paper we are concerned with the formal provability of certain true implications of Σ1-sentences. Old completeness and incompleteness results already give some information about this. For example by Σ1-completeness of PRA (primitive recursive arithmetic) every true implication of the form D → E, where D is a Σ0-sentence and E a Σ1-sentence, or D a Σ1-sentence and E a true Σ1-sentence, is provable in PRA. On the other hand, by Gödel's incompleteness theorems one can define for every suitable theory S a false Σ1-sentence Ds such that for every false Σ0-sentence E the true implication Ds → E is not provable in S, but is provable in PRA + Cons. So one sees that for a suitable fixed conclusion the provability of true implications of Σ1-sentences depends on the content of the premise.Now we ask, if and how for a suitable fixed premise the provability of true implications of Σ1-sentences depends on the conclusion. As remarked above, by Σ1-completeness of PRA this question is settled, if the premise is true. For a false premise it is answered in § 1 as follows: Let D be a false Σ1-sentence, S an extension of PRA, and S+ ≔ PRA + IAΣ1 + RFNΣ1S). Depending on D and S one can define a Σ1-sentence Es such that S+ ⊢ D → Es, but S ⊬ D → Es provided that S+ is not strong enough to refute D. (IAΣ1 denotes the scheme of the induction axiom for Σ1-formulas, and RFNΣ1(S) the uniform Σ1-reflection principle for S.)

scholarly journals On mathematical instrumentalism

2005 ◽  
Vol 70 (3) ◽  
pp. 778-794 ◽  
Author(s):  
Patrick Caldon ◽  
Aleksandar Ignjatović
Keyword(s):  
Equational Theory ◽  
Reverse Mathematics ◽  
The Other ◽  
Conservative Extension ◽  
Philosophical View ◽  
Other Hand ◽  
Primitive Recursive Arithmetic ◽  
Speed Up ◽  
Primitive Recursive

AbstractIn this paper we devise some technical tools for dealing with problems connected with the philosophical view usually called mathematical instrumentalism. These tools are interesting in their own right, independently of their philosophical consequences. For example, we show that even though the fragment of Peanos Arithmetic known as IΣ1 is a conservative extension of the equational theory of Primitive Recursive Arithmetic (PRA). IΣ1 has a super-exponential speed-up over PRA. On the other hand, theories studied in the Program of Reverse Mathematics that formalize powerful mathematical principles have only polynomial speed-up over IΣ1.

Distinction between Dolus and Culpa with reference to Arson in Zakon Sudnyj LJudem, the Vinodol Law and the Statute of Senj

De Jure ◽  
2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Daniel Haman ◽  
◽  
◽  
Keyword(s):  
Criminal Law ◽  
The Other ◽  
Legal Documents ◽  
The Third ◽  
Other Hand ◽  
Criminal Offenses ◽  
The World ◽  
The Difference ◽  
Different Levels ◽  
Better Than

The difference between intent (dolus) and negligence (culpa) was rarely emphasized in codified medieval laws and regulations. When compared to the legal statements related to intent, negligence was mentioned even more rarely. However, there are some laws that distinguished between the two concepts in terms of some specific crimes, such as arson. This paper draws attention to three medieval Slavic legal documents – the Zakon Sudnyj LJudem (ZSLJ), the Vinodol Law and the Statute of Senj. They are compared with reference to regulations regarding arson, with the focus being on arson as a crime committed intentionally or out of negligence. The ZSLJ as the oldest known Slavic law in the world shows some similarities with other medieval Slavic legal codes, especially in the field of criminal law, since most of the ZSLJ’s articles are related to criminal law. On the other hand, the Vinodol Law is the oldest preserved Croatian law and it is among the oldest Slavic codes in the world. It was written in 1288 in the Croatian Glagolitic script and in the Croatian Chakavian dialect. The third document – the Statute of Senj – regulated legal matters in the Croatian littoral town of Senj. It was written in 1388 – exactly a century after the Vinodol Law was proclaimed. When comparing the Vinodol Law and the Statute of Senj with the Zakon Sudnyj LJudem, there are clear differences and similarities, particularly in the field of criminal law. Within the framework of criminal offenses, the act of arson is important for making a distinction between intent and negligence. While the ZSLJ regulates different levels of guilt, the Vinodol Law makes no difference between dolus and culpa. On the other hand, the Statute of Senj strictly refers to negligence as a punishable crime. Even though the ZSLJ is almost half a millennium older than the Statute of Senj and around 400 years older than the Vinodol Law, this paper proves that the ZSLJ defines the guilt and the punishment for arson much better than the other two laws.

6. The why of creativity

2021 ◽  
pp. 82-96
Author(s):  
Vlad Glăveanu
Keyword(s):  
Meaning In Life ◽  
Well Being ◽  
Economic Benefits ◽  
Creative Expression ◽  
The Other ◽  
Creative People ◽  
Other Hand ◽  
The One ◽  
Health And Well Being ◽  
Different Levels

This chapter addresses why people engage in creativity. This question can be answered at different levels. On the one hand, one can refer to what motivates creative people to do what they do. On the other hand, the question addresses a deeper level, that of how societies today are built and how they, in turn, construct the meaning and value of creativity. Nowadays, people consider creativity intrinsically valuable largely because of its direct and indirect economic benefits. However, creative expression also has a role for health and well-being. Creativity also relates to meaning in life. The chapter then considers how creativity can be used for good or for evil.

Fillers, Repairs and Repetitions in the Conversations of Saudi English Speakers: Conversational Device or Disfluency Markers

2018 ◽  
Vol 10 (6) ◽  
pp. 193
Author(s):  
Yaseen A. Azi
Keyword(s):  
Discourse Analysis ◽  
Literature Review ◽  
Nonnative Speakers ◽  
Native English Speakers ◽  
The Other ◽  
English Speakers ◽  
Other Hand ◽  
Different Levels ◽  
Normal Speaking

Based on the literature review, the three patterns (fillers, repairs and repetitions) in the conversations of the native English speakers are generally regarded as results of the normal speaking between people. On the other hand, the same patterns in the conversations of the L2 speakers are always seen as a marker of disfluency and linguistic disabilities of the nonnative speakers. Therefore, this study simply focuses on finding how the three disfluency patterns are used by the Saudi English speakers from different levels of fluency. The sampling of the study includes two groups of participants from different fluency levels. Through the transcriptions and the discourse analysis of one hour recoding of the two groups, the results showed that the three patterns (fillers, repairs and repetitions) should not be generally associated with disfluency. Instead, repetitions and self-repairs have been equally used by the two groups and such patterns can be used as a conversational device. However, the filler “uh” with longer pausing can clearly predict disfluency among the Saudi English speakers. 

Effects of microbial phytase and 1,25-dihydroxycholecalciferol on the absorption of minerals from broiler chicken diets containing different levels of calcium

2002 ◽  
Vol 50 (3) ◽  
pp. 307-313 ◽  
Author(s):  
Didem Hilkat Aksakal ◽  
Tanay Bilal
Keyword(s):  
Total Phosphorus ◽  
Broiler Chicken ◽  
The Other ◽  
Broiler Chicks ◽  
Other Hand ◽  
Microbial Phytase ◽  
Utilisation Rate ◽  
Positive Effect ◽  
P Absorption ◽  
Different Levels

The aim of this study was to investigate the effect of various calcium: total phosphorus (Ca:tP) ratios due to addition of microbial phytase and 1,25-dihydroxycholecalciferol [1,25-(OH)2D3] on the absorption levels of minerals. In a 42-day experiment repeated three times, 144 day-old male broiler chicks (ISA 220) were divided into six groups of eight chicks each. Diets containing two different (1:1 and 2:1) Ca levels were prepared. Groups 1, 2 and 3 received a diet of 1:1 Ca:tP ratio while Groups 4, 5 and 6 a diet of 1:2 Ca:tP ratio. These diets contained 1,25-(OH)2D3 and phytase in levels of 5 µg/kg and 600 FYT/kg, respectively. The faeces was collected to analyse the absorption of minerals. At the end of the study, the absorption levels of Ca, P, Zn, Mn and Cu were increased by the addition of phytase enzyme (p < 0.05). This effect was obvious in the 3rd week. On the other hand, in the 6th week only Ca and P absorption levels were influenced positively by the addition of phytase enzyme. The results proved the positive effect of phytase, an enzyme which is used for increasing the utilisation rate of phytate P, Ca and other minerals in broilers.

scholarly journals The Effect of Using Different Levels of Red Ginseng Roots Powder on some Physiological Characteristics of Japanese Quail Males (Coturnix japonica)

2019 ◽  
Vol 32 (1) ◽  
pp. 34-38
Author(s):  
Khalid C.K. Al-Salhie ◽  
Abdulkarim M. Al- Waeli
Keyword(s):  
Japanese Quail ◽  
Control Diet ◽  
Relative Weight ◽  
The Other ◽  
Coturnix Japonica ◽  
Physiological Characteristics ◽  
Red Ginseng ◽  
Other Hand ◽  
Experimental Treatments ◽  
Different Levels

The current study was conducted to investigate the effect of adding different levels of ginseng roots to the diet on some physiological characteristics of Japanese quail males. A total of 120 Japanese quail males aged one week were used in this study. The males were randomly distributed into four experimental treatments (n=30). Each treatment was replicated three times (10 individual each). Males were fed experimental diets that were formulated to contain the same components as the control diet which contained red ginseng roots powder at levels 250, 500 and 750 mg/ kg feed  in other three experimental diets respectively. The results showed that the males of the fourth treatment recorded the lowest mean of the age of sexual puberty. While the highest average of sexual puberty age was recorded by the males of first treatment. On the other hand, the fourth treatment recorded the highest relative weight of testes compared with the other treatments at the age of 30 and 60 days. The results indicated that the males of the fourth treatment recorded highest Testosterone, FSH and LH levels compared with the other treatments at the age of 60 days. We can conclude from this study that the highest concentration of powder ginseng roots (750mg/kg feed) can promote the development of testes and increase testosterone, FSH and LH hormones in the serum of Japanese quail males.

scholarly journals New Method to Calculate the Level of Consistency of the Pauli & Kraepelin Tests

2018 ◽  
Author(s):  
Sigit Haryadi ◽  
Salma Huda California
Keyword(s):  
Mean Value ◽  
The Other ◽  
New Method ◽  
Other Hand ◽  
The Mean ◽  
Different Levels ◽  
Made In

In this paper, we proposed a modification of the measurement of the personality consistency level of the Pauli &amp; Kraepelin Test in the field of psychology, using the formula made in April 2016, by Sigit Haryadi, and named "the Harmony in Gradation" or “the Haryadi Index”. The purpose of this proposal is because the existing formula uses only the mean value of the deviation, which leads to the possibility that the result of consistency measurement on people whose facts are different levels of consistency will be considered to have the same consistency level, on the other hand, the proposed method will be more accurate and precise in terms of providing an assessment of the level of personality consistency of a person.

scholarly journals Late Archaic and Early Classical Coins from Excavation of Phanagoria

2019 ◽  
Author(s):  
М.Г. Абрамзон ◽  
А.А. Завойкин ◽  
В.Д. Кузнецов ◽  
И.А. Сапрыкина
Keyword(s):  
Chemical Composition ◽  
The Other ◽  
Late Archaic ◽  
Public Buildings ◽  
Public Building ◽  
Other Hand ◽  
Excavation Site ◽  
Different Levels

В статье впервые публикуются серебряные монеты конца 6 середины 5 в. до н.э. из раскопок Фанагории. Этот нумизматический материал имеет важное значение для уточнения датировки слоев поздней архаики ранней классики на акрополе Фанагории и открытого в них целого ряда объектов жилищ, общественных зданий, фортификационных сооружений. С другой стороны, археологический контекст находок монет позволяет корректировать хронологию некоторых типов самих монет. Для этих целей особенно важны находки монет, которые происходят из разных уровней жизни общественного здания (294), построенного во второй половине 6 в. до н.э. и с перестройками дожившего до середины 5 в. до н.э. Кроме того, большое значение имеют находки монет в слое разрушения древнейших оборонительных сооружений Фанагории (679), которые погибли ок. 480 г. до н.э. К этому же времени относится клад боспорских серебряных монет, спрятанный под стеной дома (205). В целом хронология ранних серебряных монет, найденных на раскопе Верхний город , согласуется с характеристиками этого района города в период поздней архаики ранней классики (примерно до середины 5 в. до н.э.), что позволяет, опираясь на фанагорийские материалы, четко определить рубеж, отделяющий датировки более поздних монетных типов. Публикуемая коллекция представляет собой ценный источник информации о денежном обращении ранней Фанагории, а исследование химического состава металла монет дает возможность подойти к решению вопросов об источниках серебра для ранней боспорской чеканки и атрибуции ряда выпусков. The article is the first publication of the 6th first half of the 5th century B.C. silver coins from excavations at Phanagoria. These numismatic finds are most important for the verification of the date of the Late Archaic and Early Classical layers at the acropolis of Phanagoria and a number of structures discovered there dwellings, public buildings, fortifications. On the other hand, the archaeological context of numismatic finds allows us to verify the chronology of certain types of coins. Most important in this connection are coin finds from different levels of a public building (294) erected in the second half of the 6th century B.C., which existed, after a number of reconstructions, till the middle of the 5th century B.C. There are also important coin finds from the ruined fortifications of Phanagoria (679) destroyed circa 480 B.C. A hoard of Bosporan silver coins concealed under the wall of a dwelling (205) belongs to the same period. In general, the chronology of early silver coins found in the excavation site the Upper City agrees with the features of this area in the Late Archaic and Early Classic times (approximately before 450 B.C.), which allows us to define the border dating later coin types. The collection presented here is a valuable evidence for the currency in early Phanagoria, and the study of the chemical composition of the coin alloy allows us to find out the sources of silver for the Early Bosporos coins and the attribution for a number of issues.

Formenanalyse bei Marx und ihr Verhältnis zur Systemwissenschaft / Analysis of forms by Marx and its relation to systems research

1975 ◽  
Vol 4 (3) ◽  
Author(s):  
Werner Loh
Keyword(s):  
Mathematical Logic ◽  
Empirical Analysis ◽  
The Other ◽  
Systems Research ◽  
Other Hand ◽  
Empirical Logic ◽  
Formal Concepts ◽  
And Mathematics ◽  
Different Levels

AbstractMARX’s analysis of forms and modern systems research have in common the problem of form. MARX analyzed forms by functionally relating elements to each other on different levels. Contrary to modern systems theories and Marxism-Leninism elements are for MARX forms themselves and not non-formal elementary qualities. The analysis of forms, therefore, is able to characterize its objects only relationally-functionally. On the other hand modern systems theories integrate concepts like ‚action‘ or ‚goal‘ in an elementaristic manner. The analysis of forms must be controlled by systematic concretization and totalization adequate to the problem. The formal concepts of systems research are often interpreted as logical-mathematical. Logic and mathematics are usually understood as non-empirical. Empirical analysis of forms is in need of an empirical logic and mathematics.

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