Order in Algebra and Logic

Mission Statement

  1. Introduction
    1. Mission. The Consortium for Order in Algebra and LogicOAL, throughout this document — is a research-oriented organization designed to draw into focus the manifold strengths of the discipline of Ordered Algebraic Structures, by supporting and promoting activities such as the following:
      • international workshops and conferences, as well as the research collaborations they might generate;
      • short and long-term visiting appointments and exchanges involving researchers and their PhD students.

      Further, OAL undertakes to inform researchers in the discipline of activities and accomplishments of interest, through its web site and through seasonal editions of its newsletter.

    2. Ordered Algebraic Structures. OAL regards Ordered Algebraic Structures — henceforth referred to as the Discipline — as the aggregate of mathematics which is concerned with order-theoretic features of algebraic structures, ranging from the studies of lattices and frames to real algebraic geometry; residuated lattices to positivity in functional analysis; lattice-ordered groups and MV-algebras to algebraic logic.
    3. Motivation. The Discipline is central to mathematics. Yet, over time, it has developed under the influence of mathematical ideas from a variety of neighboring areas, often making communication among researchers more difficult. Success in OAL’s mission ought to therefore be measured, in the short term, by the establishment of new and fruitful collaborations between researchers and disciplines, and, in the long run, by the wealth and scope of applications of pure research.
    4. The Future: Graduate Students. One of the reasons that the current OAL conferences — see 2.1 — came into existence was to acquaint graduate students with the strength and diversity in the discipline, and to place them in contact with experienced researchers. The developers of OAL have each had a number of PhD students who have benefited from these conferences. For at least four of these students, contact with OAL conference participants led to their placement after the PhD. All this is well and good. Now comes the next stage: that of securing the future of the Discipline through the recruitment and education of graduate students. A number of institutions have been successful at this; the developers of OAL take deserved pride in their measure of success at their home universities. There are other success stories, that should be more roundly celebrated, and OAL aims to be an instrument in this regard.
  2. Before OAL: ORD
    1. The Conferences. OAL has evolved ad hoc, through a series of conferences, under the ‘ORD’ label, through 2006. The first conference in the ORD series was held in early March, 1998, at the University of Florida (UF). Since that initial meeting, these conferences were held every year without interruption. The themes or focuses of the ORD conferences varied, year-to-year, reflecting the particular interests of the organizers.
    2. History of Support. The ORD conferences were funded by the hosting mathematics departments, with support from the appropriate overseeing academic units, as well as by private sources. These conferences enjoyed occasional support from the National Science Foundation.
  3. Modus Operandi
    1. Association and Organization. OAL is organized to function independently and without formal affiliation with any particular academic institution. At the same time, OAL aims to foster an informal network of associated research groups. The developers of the consortium are Jorge Martínez (UF) and Constantine Tsinakis (Vanderbilt). Both have had significant experience in the organization of conferences and the promotion of research in the discipline.
    2. The Conference Program. OAL aims to continue a program of conferences. The typical OAL conference remains the intimate gathering of 20 to 40 participants. On the other hand, the consortium will also sponsor larger conferences, which feature workshop components and focused tutorials aimed at graduate students. Events sponsored by OAL should promote new collaborations, as well as the placement of PhD students. The consortium encourages the publication of tutorials and proceedings, especially those featuring extended expository articles.
    3. Funding. Through the Vanderbilt Fund, OAL welcomes donations from individuals, groups, and institutions. All contributions are tax-deductible to the extent permitted by U.S. law. In general, OAL operates with ample flexibility in the disposition of contributed funds, to take advantage of developments in the discipline, in keeping with the goals and principles set out in this document.

Anyone wishing to make a donation to OAL through the Vanderbilt Fund should please contact Jorge Martinez at gnocchiverdi@math.ufl.edu.

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