scholarly journals Patterns of resemblance and Bachmann-Howard fixed points

2021 ◽  
Vol 28 (1) ◽  
Author(s):  
Anton Freund
Keyword(s):  
Fixed Points ◽  
Reverse Mathematics ◽  
Comprehension Question ◽  
Open Questions

AbstractTimothy Carlson’s patterns of resemblance employ the notion of $$\Sigma _1$$ Σ 1 -elementarity to describe large computable ordinals. It has been conjectured that a relativization of these patterns to dilators leads to an equivalence with $$\Pi ^1_1$$ Π 1 1 -comprehension (Question 27 of A. Montalbán’s “Open questions in reverse mathematics”, Bull. Symb. Log. 17(3)2011, 431-454). In the present paper we prove this conjecture. The crucial direction of the equivalence (towards $$\Pi ^1_1$$ Π 1 1 -comprehension) is reduced to a previous result of the author, which is concerned with relativizations of the Bachmann-Howard ordinal.

Combinatorial principles weaker than Ramsey's Theorem for pairs

2007 ◽  
Vol 72 (1) ◽  
pp. 171-206 ◽  
Author(s):  
Denis R. Hirschfeldt ◽  
Richard A. Shore
Keyword(s):  
Reverse Mathematics ◽  
The Other ◽  
Base System ◽  
Ramsey's Theorem ◽  
Open Questions ◽  
Ramsey’S Theorem ◽  
Combinatorial Principles ◽  
Points Of View ◽  
The One ◽  
Infinite Linear

AbstractWe investigate the complexity of various combinatorial theorems about linear and partial orders, from the points of view of computability theory and reverse mathematics. We focus in particular on the principles ADS (Ascending or Descending Sequence), which states that every infinite linear order has either an infinite descending sequence or an infinite ascending sequence, and CAC (Chain-AntiChain), which states that every infinite partial order has either an infinite chain or an infinite antichain. It is wellknown that Ramsey's Theorem for pairs () splits into a stable version () and a cohesive principle (COH). We show that the same is true of ADS and CAC, and that in their cases the stable versions are strictly weaker than the full ones (which is not known to be the case for and ). We also analyze the relationships between these principles and other systems and principles previously studied by reverse mathematics, such as WKL0, DNR, and BΣ2. We show, for instance, that WKL0 is incomparable with all of the systems we study. We also prove computability-theoretic and conservation results for them. Among these results are a strengthening of the fact, proved by Cholak, Jockusch, and Slaman, that COH is -conservative over the base system RCA0. We also prove that CAC does not imply DNR which, combined with a recent result of Hirschfeldt, Jockusch. Kjos-Hanssen, Lempp, and Slaman, shows that CAC does not imply (and so does not imply ). This answers a question of Cholak, Jockusch, and Slaman.Our proofs suggest that the essential distinction between ADS and CAC on the one hand and on the other is that the colorings needed for our analysis are in some way transitive. We formalize this intuition as the notions of transitive and semitransitive colorings and show that the existence of homogeneous sets for such colorings is equivalent to ADS and CAC, respectively. We finish with several open questions.

scholarly journals SEPARATING PRINCIPLES BELOW RAMSEY'S THEOREM FOR PAIRS

2013 ◽  
Vol 13 (02) ◽  
pp. 1350007 ◽  
Author(s):  
MANUEL LERMAN ◽  
REED SOLOMON ◽  
HENRY TOWSNER
Keyword(s):  
Big Five ◽  
Reverse Mathematics ◽  
Ramsey's Theorem ◽  
Open Questions ◽  
Ramsey’S Theorem

In recent years, there has been a substantial amount of work in reverse mathematics concerning natural mathematical principles that are provable from RT, Ramsey's Theorem for Pairs. These principles tend to fall outside of the "big five" systems of reverse mathematics and a complicated picture of subsystems below RT has emerged. In this paper, we answer two open questions concerning these subsystems, specifically that ADS is not equivalent to CAC and that EM is not equivalent to RT.

Open Questions in Reverse Mathematics

2011 ◽  
Vol 17 (3) ◽  
pp. 431-454 ◽  
Author(s):  
Antonio Montalbán
Keyword(s):  
Reverse Mathematics ◽  
Background Information ◽  
Open Questions ◽  
Open Question

AbstractWe present a list of open questions in reverse mathematics, including some relevant background information for each question. We also mention some of the areas of reverse mathematics that are starting to be developed and where interesting open question may be found.

scholarly journals OPEN QUESTIONS ABOUT RAMSEY-TYPE STATEMENTS IN REVERSE MATHEMATICS

2016 ◽  
Vol 22 (2) ◽  
pp. 151-169 ◽  
Author(s):  
LUDOVIC PATEY
Keyword(s):  
Reverse Mathematics ◽  
Ramsey's Theorem ◽  
The Past ◽  
Open Questions ◽  
Ramsey’S Theorem ◽  
Ramsey Type ◽  
Infinite Set

AbstractRamsey’s theorem states that for any coloring of then-element subsets of ℕ with finitely many colors, there is an infinite setHsuch that alln-element subsets ofHhave the same color. The strength of consequences of Ramsey’s theorem has been extensively studied in reverse mathematics and under various reducibilities, namely, computable reducibility and uniform reducibility. Our understanding of the combinatorics of Ramsey’s theorem and its consequences has been greatly improved over the past decades. In this paper, we state some questions which naturally arose during this study. The inability to answer those questions reveals some gaps in our understanding of the combinatorics of Ramsey’s theorem.

What’s Next?

2011 ◽  
Vol 23 (1) ◽  
pp. 60-63 ◽  
Author(s):  
Peter Vorderer
Keyword(s):  
Cultural Differences ◽  
Factor Model ◽  
New Developments ◽  
Theoretical Concepts ◽  
Open Questions ◽  
Entertainment Products ◽  
Entertainment Theory

This paper points to new developments in the context of entertainment theory. Starting from a background of well-established theories that have been proposed and elaborated mainly by Zillmann and his collaborators since the 1980s, a new two-factor model of entertainment is introduced. This model encompasses “enjoyment” and “appreciation” as two independent factors. In addition, several open questions regarding cultural differences in humans’ responses to entertainment products or the usefulness of various theoretical concepts like “presence,” “identification,” or “transportation” are also discussed. Finally, the question of why media users are seeking entertainment is brought to the forefront, and a possibly relevant need such as the “search for meaningfulness” is mentioned as a possible major candidate for such an explanation.

Dose Tracker Application for Collecting Medication Use Data from International Space Station Crew

2020 ◽  
Vol 91 (1) ◽  
pp. 41-45 ◽  
Author(s):  
Virginia. E. Wotring ◽  
LaRona K. Smith
Keyword(s):  
Data Collection ◽  
International Space Station ◽  
Sleep Disturbances ◽  
Space Station ◽  
Medication Use ◽  
International Space ◽  
Flight Data ◽  
Open Questions ◽  
Share Data ◽  
Usability Feedback

INTRODUCTION: There are knowledge gaps in spaceflight pharmacology with insufficient in-flight data to inform future planning. This effort directly addressed in-mission medication use and also informed open questions regarding spaceflight-associated changes in pharmacokinetics (PK) and/or pharmacodynamics (PD).METHODS: An iOS application was designed to collect medication use information relevant for research from volunteer astronaut crewmembers: medication name, dose, dosing frequency, indication, perceived efficacy, and side effects. Leveraging the limited medication choices aboard allowed a streamlined questionnaire. There were 24 subjects approved for participation.RESULTS: Six crewmembers completed flight data collection and five completed ground data collection before NASA’s early study discontinuation. There were 5766 medication use entries, averaging 20.6 ± 8.4 entries per subject per flight week. Types of medications and their indications were similar to previous reports, with sleep disturbances and muscle/joint pain as primary drivers. Two subjects treated prolonged skin problems. Subjects also used the application in unanticipated ways: to note drug tolerance testing or medication holiday per research protocols, and to share data with flight surgeons. Subjects also provided usability feedback on application design and implementation.DISCUSSION: The volume of data collected (20.6 ± 8.4 entries per subject per flight week) is much greater than was collected previously (<12 per person per entire mission), despite user criticisms regarding app usability. It seems likely that improvements in a software-based questionnaire application could result in a robust data collection tool that astronauts find more acceptable, while simultaneously providing researchers and clinicians with useful data.Wotring VE, Smith LK. Dose tracker application for collecting medication use data from International Space Station crew. Aerosp Med Hum Perform. 2020; 91(1):41–45.

DAMPAK PROGRAM DIKLAT ONLINE TIK GURU PUSTEKKOM TERHADAP AKSESBILITAS KONTEN PEMBELAJARAN PADA FITUR RUMAH BELAJAR

2018 ◽  
Vol 19 (2) ◽  
pp. 84
Author(s):  
Eni Susilawati
Keyword(s):  
Teacher Training ◽  
Quantitative Research ◽  
Online Training ◽  
Research Approach ◽  
Intensity Level ◽  
Web Based ◽  
Learning Content ◽  
Open Questions ◽  
Ict Training ◽  
The Impact

The research objective is to analyze the impact of the participation of online  ICT teacher training to increase the number of accessibility the learning content of features in Rumah Belajar. This research used the quantitative research approach with descriptive quantitative analysis methods to be able to describe how the increase in accessibility features of Rumah Belajar and utilization in learning in school. Samples were selected in this study are all online training participants at 15 locations online training that has been conducted by Pustekkom in 2015 and 2016 in 2015. The data was collected using a questionnaire and a list of open questions in accordance with the purpose of research. The results showed that 1) online ICT teacher training participants, after completing the Pustekkom  training online  using become more motivated to access other feature in Rumah Belajar; 2) The order of the percentage of the intensity level of accessibility to the other features of Rumah Belajar are: Sumber Belajar 23%, BSE 23%, Bank Soal 21%, Kelas Maya 13%, Lab Maya 6%, Karya Guru 4%, Wahana Jelajah Angkasa 4%, Peta Budaya 4% and Karya Komunitas 2%, and ICT training online using the application PKB Rumah Belajar can be used as a reference for efforts to develop a web-based learning applications, in particular for the development of Rumah belajar portal belongs Pustekkom Kemendikbud. Tujuan penelitian yaitu untuk menganalisis dampak keikutsertaan diklat online  TIK guru Belajar terhadap peningkatan jumlah aksebilitas konten pembelajaran pada fitur-fitur rumah belajar. Penelitian ini menggunakan pendekatan penelitian kuantitatif dengan metode analisis kuantitatif secara deskriptif untuk bisa menggambarkan bagaimana peningkatan aksesbilitas fitur-fitur rumah belajar dan pemanfaatannya dalam pembelajaran di sekolah. Sampel yang dipilih dalam penelitian ini adalah semua peserta diklat online  pada 15 lokasi diklat online yang telah dilaksanakan oleh Pustekkom pada tahun 2015 dan 2016. Pengumpulan data menggunakan kuesioner dan daftar pertanyaan terbuka sesuai dengan tujuan penelitian. Hasil penelitian menunjukkan bahwa 1) peserta diklat online TIK Guru, setelah mengikuti diklat online Pustekkom, menjadi lebih termotivasi untuk mengakses fitur-fitur lainnya dalam Rumah Belajar; 2) Urutan prosentase tingkat intensitas aksesbilitas terhadap fitur-fitur Rumbel selain Pengembangan Keprofesian berkelanjutan (PKB) adalah: Sumber Belajar 23%, Buku Sekolah Elektronik (BSE) 23%, Bank Soal 21%, Kelas Maya 13%, Lab Maya 6%, Karya Guru 4%, Wahana Jelajah Angkasa 4%, Peta Budaya 4% dan Karya Komunitas 2%; dan 3) diklat online TIK menggunakan aplikasi PKB. Rumah belajar bisa dijadikan referensi bagi upaya pengembangan aplikasi pembelajaran berbasis web, khususnya bagi pengembangan portal Rumah Belajar milik Pustekkom Kemendikbud.

Revisiting the High-Pressure Properties of the Metal-Organic Frameworks ZIF-8 and ZIF-67

2020 ◽  
Author(s):  
Pia Vervoorts ◽  
Stefan Burger ◽  
Karina Hemmer ◽  
Gregor Kieslich
Keyword(s):  
High Pressure ◽  
State Of The Art ◽  
Energy Landscape ◽  
Structural Flexibility ◽  
Zeolitic Imidazolate Frameworks ◽  
Stimuli Responsive ◽  
X Ray Diffraction ◽  
X Ray ◽  
Open Questions ◽  
Metal Organic

The zeolitic imidazolate frameworks ZIF-8 and ZIF-67 harbour a series of fascinating stimuli responsive properties. Looking at their responsitivity to hydrostatic pressure as stimulus, open questions exist regarding the isotropic compression with non-penetrating pressure transmitting media. By applying a state-of-the-art high-pressure powder X-ray diffraction setup, we revisit the high-pressure behaviour of ZIF-8 and ZIF-67 up to <i>p</i> = 0.4 GPa in small pressure increments. We observe a drastic, reversible change of high-pressure powder X-ray diffraction data at <i>p</i> = 0.3 GPa, discovering large volume structural flexibility in ZIF-8 and ZIF-67. Our results imply a shallow underlying energy landscape in ZIF-8 and ZIF-67, an observation that might point at rich polymorphism of ZIF-8 and ZIF-67, similar to ZIF-4(Zn).<br>

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