Two further combinatorial theorems equivalent to the 1-consistency of peano arithmetic

1983 ◽  
Vol 48 (4) ◽  
pp. 1090-1104 ◽  
Author(s):  
Peter Clote ◽  
Kenneth Mcaloon
Keyword(s):  
Peano Arithmetic ◽  
Infinite Subset ◽  
Linear Ordering ◽  
Tree Property ◽  
Preceding Theorem ◽  
Linear Orderings ◽  
Finite Set ◽  
The One ◽  
König’S Lemma

We give two new finite combinatorial statements which are independent of Peano arithmetic, using the methods of Kirby and Paris [6] and Paris [12]. Both are in fact equivalent over Peano arithmetic (denoted by P) to its 1-consistency. The first involves trees and the second linear orderings. Both were “motivated” by anti-basis theorems of Clote (cf. [1], [2]). The one involving trees, however, is not unrelated to the Kirby-Paris characterization of strong cuts in terms of the tree property [6], but, in fact, comes directly from König's lemma, of which it is a miniaturization. (See the remark preceding Theorem 3 below.) The resulting combinatorial statement is easily seen to imply the independent statement discovered by Mills [11], but it is not clear how to show their equivalence over Peano arithmetic without going through 1-consistency. The one involving linear orderings miniaturizes the property of infinite sets X that any linear ordering of X is isomorphic to ω or ω* on some infinite subset of X. Both statements are analogous to Example 2 of [12] and involve the notion of dense [12] or relatively large [14] finite set.We adopt the notations and definitions of [6] and [12]. We shall in particular have need of the notions of semiregular, regular and strong initial segments and of indicators.

scholarly journals ALGEBRAIC LINEAR ORDERINGS

2011 ◽  
Vol 22 (02) ◽  
pp. 491-515 ◽  
Author(s):  
S. L. BLOOM ◽  
Z. ÉSIK
Keyword(s):  
Order Type ◽  
Linear Ordering ◽  
Type Result ◽  
First Order ◽  
Linear Orderings ◽  
Context Free Language ◽  
Categorical Algebra ◽  
Context Free ◽  
Free Language

An algebraic linear ordering is a component of the initial solution of a first-order recursion scheme over the continuous categorical algebra of countable linear orderings equipped with the sum operation and the constant 1. Due to a general Mezei-Wright type result, algebraic linear orderings are exactly those isomorphic to the linear ordering of the leaves of an algebraic tree. Using Courcelle's characterization of algebraic trees, we obtain the fact that a linear ordering is algebraic if and only if it can be represented as the lexicographic ordering of a deterministic context-free language. When the algebraic linear ordering is a well-ordering, its order type is an algebraic ordinal. We prove that the Hausdorff rank of any scattered algebraic linear ordering is less than ωω. It follows that the algebraic ordinals are exactly those less than ωωω.

scholarly journals On computable self-embeddings of computable linear orderings

2009 ◽  
Vol 74 (4) ◽  
pp. 1352-1366 ◽  
Author(s):  
Rodney G. Downey ◽  
Bart Kastermans ◽  
Steffen Lempp
Keyword(s):  
Open Problem ◽  
Linear Ordering ◽  
Linear Orderings ◽  
Precise Characterization

AbstractWe solve a longstanding question of Rosenstein, and make progress toward solving a long-standing open problem in the area of computable linear orderings by showing that every computable η-like linear ordering without an infinite strongly η-like interval has a computable copy without nontrivial computable self-embedding.The precise characterization of those computable linear orderings which have computable copies without nontrivial computable self-embedding remains open.

scholarly journals Synthesis and Polymerization Kinetics of Rigid Tricyanate Ester

Polymers ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 1686
Author(s):  
Andrey Galukhin ◽  
Roman Nosov ◽  
Ilya Nikolaev ◽  
Elena Melnikova ◽  
Daut Islamov ◽  
...  
Keyword(s):  
Kinetic Analysis ◽  
Single Step ◽  
Polymerization Kinetics ◽  
Scanning Calorimetry ◽  
Modulated Differential Scanning Calorimetry ◽  
Diffusion Controlled ◽  
Polymerization Product ◽  
The One ◽  
Kinetics Of

A new rigid tricyanate ester consisting of seven conjugated aromatic units is synthesized, and its structure is confirmed by X-ray analysis. This ester undergoes thermally stimulated polymerization in a liquid state. Conventional and temperature-modulated differential scanning calorimetry techniques are employed to study the polymerization kinetics. A transition of polymerization from a kinetic- to a diffusion-controlled regime is detected. Kinetic analysis is performed by combining isoconversional and model-based computations. It demonstrates that polymerization in the kinetically controlled regime of the present monomer can be described as a quasi-single-step, auto-catalytic, process. The diffusion contribution is parameterized by the Fournier model. Kinetic analysis is complemented by characterization of thermal properties of the corresponding polymerization product by means of thermogravimetric and thermomechanical analyses. Overall, the obtained experimental results are consistent with our hypothesis about the relation between the rigidity and functionality of the cyanate ester monomer, on the one hand, and its reactivity and glass transition temperature of the corresponding polymer, on the other hand.

Towards a computational theory of social groups: A finite set of cognitive primitives for representing any and all social groups in the context of conflict

2021 ◽  
pp. 1-62
Author(s):  
David Pietraszewski
Keyword(s):  
Social Group ◽  
Group Representation ◽  
Social Groups ◽  
Study Groups ◽  
Human Mind ◽  
Computational Theory ◽  
Mistaken Belief ◽  
Finite Set ◽  
The One ◽  
Definition Of

Abstract We don't yet have adequate theories of what the human mind is representing when it represents a social group. Worse still, many people think we do. This mistaken belief is a consequence of the state of play: Until now, researchers have relied on their own intuitions to link up the concept social group on the one hand, and the results of particular studies or models on the other. While necessary, this reliance on intuition has been purchased at considerable cost. When looked at soberly, existing theories of social groups are either (i) literal, but not remotely adequate (such as models built atop economic games), or (ii) simply metaphorical (typically a subsumption or containment metaphor). Intuition is filling in the gaps of an explicit theory. This paper presents a computational theory of what, literally, a group representation is in the context of conflict: it is the assignment of agents to specific roles within a small number of triadic interaction types. This “mental definition” of a group paves the way for a computational theory of social groups—in that it provides a theory of what exactly the information-processing problem of representing and reasoning about a group is. For psychologists, this paper offers a different way to conceptualize and study groups, and suggests that a non-tautological definition of a social group is possible. For cognitive scientists, this paper provides a computational benchmark against which natural and artificial intelligences can be held.

scholarly journals Congruence pairs of principal MS-algebras and perfect extensions

2020 ◽  
Vol 70 (6) ◽  
pp. 1275-1288
Author(s):  
Abd El-Mohsen Badawy ◽  
Miroslav Haviar ◽  
Miroslav Ploščica
Keyword(s):  
Boolean Algebra ◽  
Congruence Lattices ◽  
Descriptive Solution ◽  
The One ◽  
Special Case ◽  
Congruence Pair

AbstractThe notion of a congruence pair for principal MS-algebras, simpler than the one given by Beazer for K2-algebras [6], is introduced. It is proved that the congruences of the principal MS-algebras L correspond to the MS-congruence pairs on simpler substructures L°° and D(L) of L that were associated to L in [4].An analogy of a well-known Grätzer’s problem [11: Problem 57] formulated for distributive p-algebras, which asks for a characterization of the congruence lattices in terms of the congruence pairs, is presented here for the principal MS-algebras (Problem 1). Unlike a recent solution to such a problem for the principal p-algebras in [2], it is demonstrated here on the class of principal MS-algebras, that a possible solution to the problem, though not very descriptive, can be simple and elegant.As a step to a more descriptive solution of Problem 1, a special case is then considered when a principal MS-algebra L is a perfect extension of its greatest Stone subalgebra LS. It is shown that this is exactly when de Morgan subalgebra L°° of L is a perfect extension of the Boolean algebra B(L). Two examples illustrating when this special case happens and when it does not are presented.

scholarly journals Insights into Mechanical Properties of the 1980 Irpinia Fault System from the Analysis of a Seismic Sequence

Geosciences ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 28
Author(s):  
Gaetano Festa ◽  
Guido Maria Adinolfi ◽  
Alessandro Caruso ◽  
Simona Colombelli ◽  
Grazia De Landro ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Early Warning Systems ◽  
Fault System ◽  
Minimum Size ◽  
Double Difference ◽  
Warning Systems ◽  
Initiation Mechanism ◽  
Earthquake Early Warning Systems ◽  
The One

Seismic sequences are a powerful tool to locally infer geometrical and mechanical properties of faults and fault systems. In this study, we provided detailed location and characterization of events of the 3–7 July 2020 Irpinia sequence (southern Italy) that occurred at the northern tip of the main segment that ruptured during the 1980 Irpinia earthquake. Using an autocorrelation technique, we detected more than 340 events within the sequence, with local magnitude ranging between −0.5 and 3.0. We thus provided double difference locations, source parameter estimation, and focal mechanisms determination for the largest quality events. We found that the sequence ruptured an asperity with a size of about 800 m, along a fault structure having a strike compatible with the one of the main segments of the 1980 Irpinia earthquake, and a dip of 50–55° at depth of 10.5–12 km and 60–65° at shallower depths (7.5–9 km). Low stress drop release (average of 0.64 MPa) indicates a fluid-driven initiation mechanism of the sequence. We also evaluated the performance of the earthquake early warning systems running in real-time during the sequence, retrieving a minimum size for the blind zone in the area of about 15 km.

scholarly journals Mineralogical and Geochemical Characterization of Gold Mining Tailings and Their Potential to Generate Acid Mine Drainage (Minas Gerais, Brazil)

Minerals ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 39
Author(s):  
Mariana Lemos ◽  
Teresa Valente ◽  
Paula Marinho Reis ◽  
Rita Fonseca ◽  
Itamar Delbem ◽  
...  
Keyword(s):  
Acid Mine Drainage ◽  
Mine Drainage ◽  
Minas Gerais ◽  
Acid Mine ◽  
Fine Grain ◽  
Mineralogical Characteristics ◽  
Tailing Dams ◽  
The One ◽  
And Control

For more than 30 years, sulfide gold ores were treated in metallurgic plants located in Nova Lima, Minas Gerais, Brazil, and accumulated in the Cocoruto tailings dam. Both flotation and leaching tailings from a deactivated circuit, as well as roasted and leaching tailings from an ongoing plant, were studied for their acid mine drainage potential and elements’ mobility. Detailed characterization of both tailings types indicates the presence of fine-grain size material hosting substantial amounts of sulfides that exhibit distinct geochemical and mineralogical characteristics. The samples from the ongoing plant show high grades of Fe in the form of oxides, cyanide, and sulfates. Differently, samples from the old circuit shave higher average concentrations of Al (0.88%), Ca (2.4%), Mg (0.96%), and Mn (0.17%), present as silicates and carbonates. These samples also show relics of preserved sulfides, such as pyrite and pyrrhotite. Concentrations of Zn, Cu, Au, and As are higher in the tailings of the ongoing circuit, while Cr and Hg stand out in the tailings of the deactivated circuit. Although the obtained results show that the sulfide wastes do not tend to generate acid mine drainage, leaching tests indicate the possibility of mobilization of toxic elements, namely As and Mn in the old circuit, and Sb, As, Fe, Ni, and Se in the tailings of the plant that still works. This work highlights the need for proper management and control of tailing dams even in alkaline drainage environments such as the one of the Cocoruto dam. Furthermore, strong knowledge of the tailings’ dynamics in terms of geochemistry and mineralogy would be pivotal to support long-term decisions on wastes management and disposal.

Preparation and characterization of tannin-based adhesives reinforced with cellulose nanofibrils for wood bonding

Holzforschung ◽  
2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Uasmim Lira Zidanes ◽  
Matheus Cordazzo Dias ◽  
Mário Sérgio Lorenço ◽  
Elesandra da Silva Araujo ◽  
Maryella Júnnia Ferreira e Silva ◽  
...  
Keyword(s):  
Cellulose Nanofibrils ◽  
Glue Line ◽  
Mechanical Resistance ◽  
Thermogravimetric Analyses ◽  
Humidity Resistance ◽  
Wood Bonding ◽  
Toona Ciliata ◽  
Solids Content ◽  
The One

AbstractAdhesives based on vegetable tannins are already a reality in the market. However, their use is still limited due to their low mechanical resistance and weak humidity resistance. Cellulose nanofibrils (CNFs) are being used as reinforcing materials in various composites, resulting in an improvement of mechanical proprieties in general. The objective of this work was to evaluate the incorporation of CNFs in adhesives made of tannins obtained from the Angico tree (Anadenanthera peregrine). Concentrations of nanofibrils at 1, 5, and 10% were added to the adhesives on a dry basis. Tests of viscosity, pH, solids content, and gel time were performed to determine the physical proprieties of the adhesives. The Attenuated Total Reflectance Fourier Transform Infrared Spectroscopy (ATR-FTIR) and Raman spectra measurements were also determined to understand the interaction between tannins and CNFs. Thermogravimetric analyses (TGA) were carried out to determine the thermal resistance of the composite. The FTIR and Raman characterization identified some differences in the peaks in the chemical composition of the adhesives with different percentages of CNFs. The adhesives showed no different decomposition in the thermogravimetric analyses. The shear strength in the glue line of the adhesive with 5% of CNFs in Toona ciliata woods was determined. Among all the adhesives analyzed, the one with 5% of CNFs produced an improvement in the mechanical resistance and humidity resistance on the glue line.

scholarly journals The Small and Efficient Language Network of Polyglots and Hyper-polyglots

2020 ◽  
Vol 31 (1) ◽  
pp. 62-76
Author(s):  
Olessia Jouravlev ◽  
Zachary Mineroff ◽  
Idan A Blank ◽  
Evelina Fedorenko
Keyword(s):  
Foreign Language ◽  
Language Processing ◽  
Default Mode Network ◽  
Individual Level ◽  
Neural Architecture ◽  
Initial Characterization ◽  
The One ◽  
Multiple Languages ◽  
Language Network

Abstract Acquiring a foreign language is challenging for many adults. Yet certain individuals choose to acquire sometimes dozens of languages and often just for fun. Is there something special about the minds and brains of such polyglots? Using robust individual-level markers of language activity, measured with fMRI, we compared native language processing in polyglots versus matched controls. Polyglots (n = 17, including nine “hyper-polyglots” with proficiency in 10–55 languages) used fewer neural resources to process language: Their activations were smaller in both magnitude and extent. This difference was spatially and functionally selective: The groups were similar in their activation of two other brain networks—the multiple demand network and the default mode network. We hypothesize that the activation reduction in the language network is experientially driven, such that the acquisition and use of multiple languages makes language processing generally more efficient. However, genetic and longitudinal studies will be critical to distinguish this hypothesis from the one whereby polyglots’ brains already differ at birth or early in development. This initial characterization of polyglots’ language network opens the door to future investigations of the cognitive and neural architecture of individuals who gain mastery of multiple languages, including changes in this architecture with linguistic experiences.

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