This book continues the series of volumes containing reprints of the papers in the original Cabal Seminar volumes of the Springer Lecture Notes in Mathematics series [Cabal i, Cabal ii, Cabal iii, Cabal iv], unpublished material, and new papers. The first volume, [Cabal I], contained papers on games, scales and Suslin cardinals. In this volume, we continue with Parts III and IV of the project: Wadge degrees and pointclasses and Projective ordinals. As in our first volume, each of the parts contains an introductory survey (written by Alessandro Andretta and Alain Louveau for Part III and by Steve Jackson for Part IV) putting the papers into a present-day context.

In addition to the reprinted papers, this volume contains papers by Steel (More measures from AD) and Martin (Projective sets and cardinal numbers) that date back to the period of the original Cabal publications but were not included in the old volumes. Jackson contributed a new paper Regular cardinals without the weak partition property with recent results that fit well with the topic of Part IV. The paper Early investigations of the degrees of Borel sets by Wadge is a historical overview of the process of the development of the basic theory of the Wadge degrees. Table 1 gives an overview of the papers in this volume with their original references.

As emphasized in our first volume, our project is not to be understood as a historical edition of old papers. In the retyping process, we uniformized and modernized notation and numbering of sections and theorems.

In this paper, I give an overview/summary of the techniques used, and the results derived, in my 1984 PhD dissertation, Reducibility and Determinateness on the Baire Space. In particular, I focus on the calculation of the order type (and structure) of the collection of degrees of Borel sets.

§1 Introduction. I would like in this article to present a overview of the main results of my PhD dissertation, and of the game and other techniques used to derive them.

My first thought was to print the entire dissertation but I quickly realized that it was too long—about ten times too long! Hopefully, this condensed version will still be useful. In producing such a drastically shortened account, I have omitted detailed proofs, and many less important or intermediate results. Also, the remaining definitions and results are for the most part given informally.

In writing this I have in mind, first, colleagues (whether in Mathematics or Computing) who are not familiar with descriptive set theory but nevertheless would like to learn about “Wadge Degrees”. To make the material accessible to these readers I have included some basic information about, say, Borel sets that will be very familiar to Cabal insiders. However, my hope is that even experts in descriptive set theory may learn something, if not about my results, at least about the manner in which they were discovered. In particular, I would like to give some ‘classic’ notions, such as Boolean set operations, the attention they deserve.

This chapter proposes exercises and projects based on CouchDB, a recent database system which relies on many of the concepts presented so far in this book. In brief:

1. CouchDB adopts a semistructured data model, based on the JSON (JavaScript Object Notation) format; JSON offers a lightweight alternative to XML;

2. A database in CouchDB is schema-less: the structure of the JSON documents may vary at will depending on their specific features;

3. In order to cope with the absence of constraint that constitutes the counterpart of this flexibility, CouchDB proposes an original approach, based on structured materialized views that can be produced from document collections;

4. Views are defined with the MapReduce paradigm, allowing both a parallel computation and incremental maintenance of their content;

5. Finally, the system aspects of CouchDB illustrate most of the distributed data management techniques covered in the last part of the present book: distribution based on consistent hashing, support for data replication and reconciliation, horizontal scalability, parallel computing, and so forth.

CouchDB is representative of the emergence of so-called key-value store systems that give up many features of the relational model, including schema, structured querying, and consistency guarantees, in favor of flexible data representation, simplicity and scalability. It illustrates the “No[tOnly]SQL” trend with an original and consistent approach to large-scale management of “documents” viewed as autonomous, rich pieces of information that can be managed independently, in contrast with relational databases, which take the form of a rich graph of interrelated flat tuples.

INTRODUCTION

This chapter introduces XPath and XQuery, two related languages that respectively serve to navigate and query XML documents. XPath is actually a subset of XQuery. Both languages, specified by theW3C, are tightly associated and share in particular the same conceptual modeling of XML documents. Note that the XPath fragment of XQuery has a well-identified purpose (expressing “paths” in an XML tree) and as such can be used independently in other XML processing contexts, such as inside the XSLT transformation language. XQuery uses XPath as a core language for path expressions and navigation.

XQuery is a declarative language and intends to play for XML data the role of SQL in the relational realm. At a syntactical level, it is somewhat inspired from SQL. More importantly, it is expected to benefit from a mixture of physical storage, indexing, and optimization techniques in order to retrieve its result by accessing only a small fraction of its input. XQuery constitutes therefore an appropriate choice when large XML documents or large collections of documents must be manipulated.

In this chapter, we use as running example a movies XML database. Each XML document represents one movie and is similar in structure to the sample document shown in Figure 2.1.

We begin the chapter with a bird's-eye view of XQuery principles, introducing the XML data model that supports the interpretation of path expressions and queries, and showing the main features of the two languages. We then consider in more detail XPath and XQuery in a rather informal way.

Lucene is an open-source tunable indexing platform often used for full-text indexing of Web sites. It implements an inverted index, creating posting lists for each term of the vocabulary. This chapter proposes some exercises to discover the Lucene platform and test its functionalities through its Java API.

PRELIMINARY: A LUCENE SANDBOX

We provide a simple graphical interface that lets you capture a collection of Web documents (from a given Web site), index it, and search for documents matching a keyword query. The tool is implemented with Lucene (surprise!) and helps to assess the impact of the search parameters, including ranking factors.

You can download the program from our Web site. It consists of a Java archive that can be executed right away (provided you have a decent Java installation on your computer). Figure 17.1 shows a screenshot of the main page. It allows you to

1. Download a set of documents collected from a given URL (including local addresses),

2. Index and query those documents,

3. Consult the information used by Lucene to present ranked results.

Use this tool as a preliminary contact with full text search and information retrieval. The projects proposed at the end of the chapter give some suggestions to realize a similar application.

INDEXING PLAIN TEXT WITH LUCENE – A FULL EXAMPLE

We embark now in a practical experimentation with Lucene. First, download the Java packages from the Web site http://lucene.apache.org/java/docs/.