Skip to main content Accessibility help
×
  1. Home
  2. Browse subjects
  3. Computer Science
  4. Programming Languages and Applied Logic
  5. Content listing

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

5849 results in Programming Languages and Applied Logic

Page 136 of 293

  • CHAPTER 11 - CANONICAL BASES

  • Enrique Casanovas
  • Book:
    Simple Theories and Hyperimaginaries
    Published online:
    05 March 2012
    Print publication:
    30 June 2011, pp 69-74

  • Summary

    Definition 11.1. The multiplicity of a type p(x) ∈ S(A) is the number Mlt(p) of its global nonforking extensions p(x) ∈ S(ℭ). If there is a proper class of global nonforking extensions of p, we say that p has unbounded multiplicity and we write Mlt(p) = ∞; otherwise we say that p has bounded multiplicity. A stationary type is a type of multiplicity 1. Thus over any B ⊇ A a stationary type p(x) ∈ S(A) has a unique nonforking extension q(x) ∈ S(B). We use the notation p|B for q.

    Lemma 11.2. Let T be simple. If p ∈ S(A) is stationary, then its global nonforking extension is Definable over A.

    Proof. Let p be the global nonforking extension of p, and let φ(x, y) ∈ L. We will show that p ↾ φ is A-definable. Let Δφ(y) and Δ¬φ(y) be types over A given by Corollary 5.23 for p and φ and for p and ¬φ respectively. By compactness, the conjunction ψ(y) of a finite subset of Δφ(y) is inconsistent with Δ¬φ(y). It is clear that ψ(y) defines p ↾ φ.

    Corollary 11.3. Let T be simple. If types over models are stationary, then T is stable.

    Proof. Lemma 11.2 implies that in this situation every global type is Definable.

  • CHAPTER 16 - HYPERIMAGINARY FORKING

  • Enrique Casanovas
  • Book:
    Simple Theories and Hyperimaginaries
    Published online:
    05 March 2012
    Print publication:
    30 June 2011, pp 109-120

  • Summary

    Definition 16.1. Let A be a class of hyperimaginaries and let I be a set linearly ordered by <. The sequence of hyperimaginaries (ei : i ∈ I) is indiscernible over A or it is A-indiscernible if for every n < ω, for every two increasing sequences of indices i0 < … < in and j0, < … < jn,. If A is a set, in practice we may always assume that A is a single hyperimaginary. Note that all the hyperimaginaries ei are in fact of the same sort and hence we can write ei = [ai]E for a single E.

    Lemma 16.2. Let d be a hyperimaginary.

    1. 1. Let I, J be linearly ordered infinite sets. If (ei : i ∈ I) is a d-indiscernible sequence of hyperimaginaries, then there is a d-indiscernible sequence (ci : j ∈ J) such that for every n < ω, for every two increasing sequences of indices i0 < … < in ∈ I and j0 < … < jn ∈ J,.

    2. 2. If (ei : i ∈ I) and (di : i ∈ I) are d-indiscernible sequences of hyperimaginaries and (ei : i ∈ I0) ≡d (di : i ∈ I0) for each finite subset I0 ⊆ I, then f((ei : i ∈ I)) = (di : i ∈ I) for some f ∈ Aut(ℭ/d).

Finite and Algorithmic Model Theory
  • Edited by Javier Esparza, Christian Michaux, Charles Steinhorn
  • Published online:
    01 June 2011
    Print publication:
    10 March 2011
  • Intended for researchers and graduate students in theoretical computer science and mathematical logic, this volume contains accessible surveys by leading researchers from areas of current work in logical aspects of computer science, where both finite and infinite model-theoretic methods play an important role. Notably, the articles in this collection emphasize points of contact and connections between finite and infinite model theory in computer science that may suggest new directions for interaction. Among the topics discussed are: algorithmic model theory, descriptive complexity theory, finite model theory, finite variable logic, model checking, model theory for restricted classes of finite structures, and spatial databases. The chapters all include extensive bibliographies facilitating deeper exploration of the literature and further research.

Lectures in Game Theory for Computer Scientists
  • Edited by Krzysztof R. Apt, Erich Grädel
  • Published online:
    01 June 2011
    Print publication:
    06 January 2011
  • Games provide mathematical models for interaction. Numerous tasks in computer science can be formulated in game-theoretic terms. This fresh and intuitive way of thinking through complex issues reveals underlying algorithmic questions and clarifies the relationships between different domains. This collection of lectures, by specialists in the field, provides an excellent introduction to various aspects of game theory relevant for applications in computer science that concern program design, synthesis, verification, testing and design of multi-agent or distributed systems. Originally devised for a Spring School organised by the GAMES Networking Programme in 2009, these lectures have since been revised and expanded, and range from tutorials concerning fundamental notions and methods to more advanced presentations of current research topics. This volume is a valuable guide to current research on game-based methods in computer science for undergraduate and graduate students. It will also interest researchers working in mathematical logic, computer science and game theory.

Reactive Systems
  • Modelling, Specification and Verification
  • Luca Aceto, Anna Ingólfsdóttir, Kim Guldstrand Larsen, Jiri Srba
  • Published online:
    17 March 2011
    Print publication:
    09 August 2007
  • Formal methods is the term used to describe the specification and verification of software and software systems using mathematical logic. Various methodologies have been developed and incorporated into software tools. An important subclass is distributed systems. There are many books that look at particular methodologies for such systems, e.g. CSP, process algebra. This book offers a more balanced introduction for graduate students that describes the various approaches, their strengths and weaknesses, and when they are best used. Milner's CCS and its operational semantics are introduced, together with notions of behavioural equivalence based on bisimulation techniques and with variants of Hennessy-Milner modal logics. Later in the book, the presented theories are extended to take timing issues into account. The book has arisen from various courses taught in Iceland and Denmark and is designed to give students a broad introduction to the area, with exercises throughout.

Page 136 of 293