Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

What is modal logic

TABLE OF CONTENTS Introduction Chapter I. The relation of the structure of an r.e. set to its degree. 1. Post's program and simple sets. 2. Dominating functions and quotient lattices. 3. Maximal sets and high degrees. 4. Low degrees, atomless sets, and invariant degree classes. 5. Incompleteness and completeness for noninvariant properties. Chapter II. The structure, automorphisms, and elementary theory of the r.e. sets. 6. Basic facts and splitting theorems. 7. Hh-simple sets. 8. Major subsets and r-maximal sets. 9. Automorphisms of &. 10. The elementary theory of S. Chapter III. The structure of the r.e. degrees. 11. Basic facts. 12. The finite injury priority method. 13. The infinite injury priority method. 14. The minimal pair method and lattice embeddings in R. 15. Cupping and splitting r.e. degrees. 16. Automorphisms and decidability of R.

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Recursively enumerable sets and degrees

The development of the Semantic Web, with machine-readable content, has the potential to revolutionize the World Wide Web and its uses. A Semantic Web Primer provides an introduction and guide to this continuously evolving field, describing its key ideas, languages, and technologies. Suitable for use as a textbook or for independent study by professionals, it concentrates on undergraduate-level fundamental concepts and techniques that will enable readers to proceed with building applications on their own and includes exercises, project descriptions, and annotated references to relevant online materials.The third edition of this widely used text has been thoroughly updated, with significant new material that reflects a rapidly developing field. Treatment of the different languages (OWL2, rules) expands the coverage of RDF and OWL, defining the data model independently of XML and including coverage of N3/Turtle and RDFa. A chapter is devoted to OWL2, the new W3C standard. This edition also features additional coverage of the query language SPARQL, the rule language RIF and the possibility of interaction between rules and ontology languages and applications. The chapter on Semantic Web applications reflects the rapid developments of the past few years. A new chapter offers ideas for term projects. Additional material, including updates on the technological trends and research directions, can be found at http://www.semanticwebprimer.org.

/pdf/a-semantic-web-primer-121rmyoa9a.pdf

A semantic Web primer

Preface- Acknowledgments- Introduction- I Background- Preliminaries- Computability Theory- Kolmogorov Complexity of Finite Strings- Relating Plain and Prefix-Free Complexity- Effective Reals- II Randomness of Sets- Martin-Lof Randomness- Other Notions of Effective Randomness- Algorithmic Randomness and Turing Reducibility- III Relative Randomness- Measures of Relative Randomness- The Quantity of K- and Other Degrees- Randomness-Theoretic Weakness- Lowness for Other Randomness Notions- Effective Hausdorff Dimension- IV Further Topics- Omega as an Operator- Complexity of CE Sets- References- Index

Algorithmic Randomness and Complexity

http://www.math.uchicago.edu/~drh/Papers/Papers/alg.pdf

Degree spectra and computable dimensions in algebraic structures

We 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.

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Combinatorial principles weaker than Ramsey's Theorem for pairs

This book is a rigorous introduction to classical and nonclassical logics which emphasizes deduction as a form of computation. It can be used to teach classical, modal, and intuitistic predicate logic. It also presents the logical and mathematical foundations for resolution theorem proving and Logic Programming. A distinctive feature of this book is its uniform mathematical treatment of logic, based on the tableau method of classical logic, which includes soundness, completeness, compactness, incompleteness, and the theorems of Herb Rand and Skolem-L Wenheim. The same uniform treatment is used for important areas of application in computer science and artificial intelligence. These include resolution theorem proving, Logic Programming and Prolog, Predicate Intuitionistic Logic, and Predicate Modal Logic. There is also an historical appendix and an extensive list of selected references so that both the background and more advanced developments of these subjects can be understood and pursued. This text is appropriate for upper level undergraduate and beginning graduate students.

Logic for applications

The recursively enumerable α-degrees are dense

On donne une decomposition definissable du semi-treillis superieur des degres recursivement enumerables R comme l'union disjointe d'un ideal M et un filtre fort NC

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Richard A. Shore

Papers

Degree spectra and computable dimensions in algebraic structures

Combinatorial principles weaker than Ramsey's Theorem for pairs

Logic for applications

The recursively enumerable α-degrees are dense

An algebraic decomposition of the recursively enumerable degrees and the coincidence of several degree classes with the promptly simple degrees