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Books in Mathematical logic and foundations

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Logic Colloquium '84

  • 1st Edition
  • October 10, 2011
  • J.B. Paris + 2 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 9 6 0 4 3 - 2
This proceedings volume contains most of the invited talks presented at the colloquium. The main topics treated are the model theory of arithmetic and algebra, the semantics of natural languages, and applications of mathematical logic to complexity theory. The volume contains both surveys by acknowledged experts and original research papers presenting advances in these disciplines.

Axiomatic Set Theory

  • 1st Edition
  • Volume 51
  • August 30, 2011
  • R.B. Chuaqui
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 7 1 6 2 - 2

Theory of Relations

  • 1st Edition
  • August 18, 2011
  • R. Fraïssé
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 9 6 0 4 1 - 8
The first part of this book concerns the present state of the theory of chains (= total or linear orderings), in connection with some refinements of Ramsey's theorem, due to Galvin and Nash-Williams. This leads to the fundamental Laver's embeddability theorem for scattered chains, using Nash-Williams' better quasi-orderings, barriers and forerunning.The second part (chapters 9 to 12) extends to general relations the main notions and results from order-type theory. An important connection appears with permutation theory (Cameron, Pouzet, Livingstone and Wagner) and with logics (existence criterion of Pouzet-Vaught for saturated relations). The notion of bound of a relation (due to the author) leads to important calculus of thresholds by Frasnay, Hodges, Lachlan and Shelah. The redaction systematically goes back to set-theoretic axioms and precise definitions (such as Tarski's definition for finite sets), so that for each statement it is mentioned either that ZF axioms suffice, or what other axioms are needed (choice, continuum, dependent choice, ultrafilter axiom, etc.).

Foundations of Infinitesimal Stochastic Analysis

  • 1st Edition
  • August 18, 2011
  • K.D. Stroyan + 1 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 9 6 0 4 2 - 5
This book gives a complete and elementary account of fundamental results on hyperfinite measures and their application to stochastic processes, including the *-finite Stieltjes sum approximation of martingale integrals. Many detailed examples, not found in the literature, are included. It begins with a brief chapter on tools from logic and infinitesimal (or non-standard) analysis so that the material is accessible to beginning graduate students.

Combinatory Logic

  • 1st Edition
  • Volume 65
  • June 17, 2009
  • Lev D. Beklemishev
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 9 5 4 7 7 - 6

Logic Colloquium '80

  • 1st Edition
  • June 5, 2009
  • D. van Dalen + 2 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 9 6 0 3 4 - 0
The papers appearing in this volume are part of those originally intended for presentation at the conference: Logic Colloquium '80 - European Summer Meeting of the Association for Symbolic Logic (A.S.L.) which was to takeplace in Prague, August 24·30, 1980, principally under the auspices of the Czech Academy of Sciences. There were 36 invited speakers from Western and Eastern Europe, Israel, the U.S., and the U.S.S.R. The local organizingcommittee cabled participants on July 15, 1980 to inform them that the meeting was cancelled for technical reasons; a subsequent communication stated that the cancellation was due to unforeseen circumstances lying beyond the controlof the organizing committee. The unexpected cancellation of the Prague meeting was greatly regretted, since so much care, time, and energy had been given to its advance preparation by the local organizing committee as well as by representatives of the A.S.L.and its European Committee. The late date on which cancellation took place required drastic changes of plans by speakers and participants. Last-minute efforts to reschedule the meeting elsewhere in Europe could not be realized.

Mathematical Analysis and Proof

  • 2nd Edition
  • April 30, 2009
  • David S G Stirling
  • English
  • eBook
    9 7 8 - 0 - 8 5 7 0 9 - 9 3 4 - 1
This fundamental and straightforward text addresses a weakness observed among present-day students, namely a lack of familiarity with formal proof. Beginning with the idea of mathematical proof and the need for it, associated technical and logical skills are developed with care and then brought to bear on the core material of analysis in such a lucid presentation that the development reads naturally and in a straightforward progression. Retaining the core text, the second edition has additional worked examples which users have indicated a need for, in addition to more emphasis on how analysis can be used to tell the accuracy of the approximations to the quantities of interest which arise in analytical limits.