21. Mai Gehrke's Curriculum Vita New Mexico State University Nonstandard mathematics, operators on boolean algebras, fuzzy mathematics, universal algebra, general topology, posets and lattices. http://www.math.nmsu.edu/mgehrke/mgehrke.html

Mai Gehrke Department of Mathematical Sciences Phone: (505] 646-4218 New Mexico State University Fax: (505) 646-1064 Las Cruces, NM 88003 mgehrke@nmsu.edu Office Location: Science Hall Room 232 House for rent while on sabbatical 2004-2005 Return to Faculty Page Return to Main Index PROFESSIONAL EXPERIENCE Professor, New Mexico State University, Las Cruces, New Mexico. 1/99Present Part-time consulting, Physical Science Laboratory, Las Cruces, New Mexico. 1/975/97 Visiting Professor, Vanderbilt University, Nashville, Tennessee. 8/9612/96 Visiting Lektor, University of Copenhagen, Copenhagen, Denmark. 8/93 5/00 Associate Professor, New Mexico State University, Las Cruces, New Mexico. 8/905/93 Assistant Professor, New Mexico State University, Las Cruces, New Mexico. 8/885/90 2-year position as Assistant Professor, Vanderbilt University, Nashville, Tennessee. 1/837/87 Teaching Assistant, University of Houston, Houston, Texas. Return to top of page RESEARCH INTERESTS Logic and its Applications Universal Algebra and Lattice Theory General Topology Return to top of page PUBLICATIONS Mathematical Research Publications A new proof of completeness of S4 with respect to the real line , with G. Bezhanishvili, submitted to

22. Universal Algebra From FOLDOC universal algebra. logic the model theory of firstorderequational logic union of sets «. universal «. universal algebra ». universal generalization ». universal instantiation http://lgxserver.uniba.it/lei/foldop/foldoc.cgi?universal algebra

23. Szeged Conference Conference on. universal algebra and Lattice Theory. S. Burris (Waterloo, Canada) Computers and universal algebra; C. Herrmann (Darmstadt, Germany) http://www.math.u-szeged.hu/confer/algebra/1996/algebra.htm

Conference on Universal Algebra and Lattice Theory Szeged, Hungary, July 1519, 1996 A satellite conference of the 2nd European Congress of Mathematics (Budapest, July 2127, 1996) Organized jointly with the Szeged Committee of the Hungarian Academy of Sciences Supported by Catching up with European Higher Education Fund European Mathematical Society National Committee for Technical Development Hungarian National Foundation for Scientific Research Foundation for Szeged The conference will start on July 15 (Monday) in the morning, and will conclude on July 19 (Friday) early afternoon. The participants are expected to arrive on July 14. The lectures will take place in the building of the Szeged Committee of the Hungarian Academy of Sciences which is located in the center of Szeged, near the mathematics building of the university. Scientific programme. There will be one-hour plenary invited lectures on current research in universal algebra and lattice theory, as well as in other fields of mathematics that are related to these topics, 20-minute contributed talks in parallel sections, and

24. Prof. Kaiser University of Houston Mathematical logic, universal algebra, lattice theory and logic programming. http://math.uh.edu/~klaus/

Klaus Kaiser Professor of Mathematics, University of Houston Office: 607 PGH Office Phone: (713)-743-3462 The easiest way to reach me is by sending me e-mail to kkaiser@uh.edu . Students and UH colleagues should use my other e-mail: klaus@math.uh.edu . You may also send me snail-mail via the Department of Mathematics, University of Houston, Houston, TX77204-3476. During Summer I, 2004, I will teach Math 4377, Linear Algebra and Math 1330, Elementary Functions I came to the University of Houston in 1969 with a degree from the University of Bonn. My main research interests are in Mathematical Logic, Universal Algebra, Lattice Theory and Logic Programming. Some of my papers, e.g., on quasi-universal and projective model classes are with Manfred Armbrust who retired from the University of Cologne. A paper on non-standard lattice theory is with two of my former Ph.D. students Mai Gehrke and Matt Insall . We had this paper dedicated to Abraham Robinson. Since June 1996, I am the Managing Editor of the Houston Journal of Mathematics . I got quite interested in publishing issues: At the Satellite Conference on Electronic Information and Communication in Mathematics of the International Congress of Mathematicians, Beijing, August 2002

25. Universal Algebra From FOLDOC universal algebra. logic the model theory of firstorder equational logic. FOLDOC. 2001-03-16 . Try this search on OneLook / Google. http://www.swif.uniba.it/lei/foldop/foldoc.cgi?universal algebra

26. Miguel Couceiro MALJA, Finland. universal algebra, function class and relational constraint characterizations. http://mtl.uta.fi/~mc68234/

Miguel Couceiro Address: Department of Mathematics, Statistics and Philosophy, University of Tampere, Kalevantie 4, 33014 Tampere, Finland Phone: Fax: E -mail: Miguel.couceiro@uta.fi I am a researcher and Doctoral student at MALJA graduate school in Mathematical Logic and Algebra. The graduate school operates at Universities in Tampere and Helsinki. Here is a link to our joint research seminar on finite model theory . I am under the supervision of Professor Lauri Hella (University of Tampere) and Professor Stephan Foldes ( Tampere University of Technology My research interests range from topics in Universal Algebra (clones of operations, relations and related structures) to Function Class and Relational Constraint characterizations. Here are some of my publications: Rutcor Research Report 12 - 2002, http://rutcor.rutgers.edu/ , (to appear in Discrete Applied Mathematics) http://rutcor.rutgers.edu/ on Logic and Computer Science, Szeged, Hungary, 2003, http://www.rgai.hu/kalmar2003/ On Closed Sets of Relational Constraints and Classes of Functions Closed under Variable Substitutions Rutcor Research Report 10 - 2004, http://rutcor.rutgers.edu/

27. Universal Algebra universal algebra. universal algebra is the field of mathematics that studies the ideas common to all algebraic structures. http://www.fact-index.com/u/un/universal_algebra.html

Main Page See live article Alphabetical index Universal algebra Universal algebra is the field of mathematics that studies the ideas common to all algebraic structures Table of contents 1 Basic idea 2 Examples 2.1 Groups 2.2 Modules ... 3 Further issues Basic idea From the point of view of universal algebra, an algebra is a set A together with a collection of operations on A . An n -ary operation on A is a function that takes n elements of A and returns a single element of A . Thus, a 0-ary operation (or nullary operation ) is simply an element of A , or a constant , often denoted by a letter like a . A 1-ary operation (or unary operation ) is simply a function from A to A , often denoted by a symbol placed in front of its argument, like ~ x . A 2-ary operation (or binary operation ) is often denoted by a symbol placed between its arguments, like x y . Operations of higher or unspecified arity are usually denoted by function symbols, with the arguments placed in parentheses and separated by commas, like f x y z ) or f x x n After the operations have been specified, the nature of the algebra can be further limited by axioms , which in universal algebra must take the form of equational laws. An example is the

28. Conferences In General Algebra And Related Fields 2004 ASL European Summer Meeting (Logic Colloquium 04) (with a special session in universal algebra), Torino, Italy, July 2531, 2004. 68. http://spot.colorado.edu/~kearnes/conf.html

Conferences in General Algebra and Related Fields DIMACS Working Group on Applications of Order Theory to Homeland Defense and Computer Security , Rutgers, New Jersey, September 30, 2004. DIMACS Workshop on Applications of Order Theory to Homeland Defense and Computer Security , Rutgers, New Jersey, September 28-29, 2004. Algebras, Lattices, Varieties - A Conference in Honor of Walter Taylor , Boulder CO, August 15-18, 2004. 2004 ASL European Summer Meeting (Logic Colloquium '04) (with a special session in Universal Algebra), Torino, Italy, July 25-31, 2004. 68. Arbeitstagung Allgemeine Algebra (68th Workshop on General Algebra) , University of Dresden, Germany, June 10-13, 2004. International Conference on Residuated Structures and Many Valued Logics, Patras University, Greece, June 2-5, 2004. 67. Arbeitstagung Allgemeine Algebra (67th Workshop on General Algebra) , University of Potsdam, Germany, March 26-28, 2004. Joint Mathematics Meetings (AMS-MAA-ASL-AWM-NAM-SIAM) (with a Special Session on Lattice Theory and Ordered Sets), Phoenix AZ, January 7-10, 2004. Winter Meeting of the Canadian Mathematical Society, 2003

29. The Cornell Library Historical Mathematics Monographs Document name A treatise on universal algebra, with applications, Go to page NA Production Note. http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?did=01950001&se

30. Universal Algebra In Combinatory Logic universal algebra in Combinatory Logic. Beatrice Amrhein. Introduction. Constructing new algebras from given ones, plays a central role in universal algebra. http://www.isbe.ch/~amrhein/diss/diss.html

Universal Algebra in Combinatory Logic Beatrice Amrhein Introduction The strong influence of computer science on mathematics is causing a growing interest in the concept of functions as algorithms. Considering functions as operations or rules in their full generality, they can be applied to any argument. For example, we may think of a function as a program that operates on other programs. In particular, self application is allowed. combinatory completeness : Any applicative expression built up from functions may not only be regarded as a function, but also represented by a combinator. Models of this theory are called combinatory algebras . They are of the form , where A is some set, a binary operation on A and where combinatory completeness is satisfied. They arise whenever a mathematical structure is furnished with a notion of internal computability. It was in the same decade that it became clear that (classical) algebra deals not primarily with the manipulation of sums and products of numbers, but with sums and products of elements of any sort - under the assumption that these operations satisfy the appropriate basic axioms . This was the starting point of universal algebra , where the objects of interest - the structures - were presented by use of axioms over operations and morphisms between them.

31. Universal Algebra - Encyclopedia Article About Universal Algebra. Free Access, N encyclopedia article about universal algebra. universal algebra in Free online English dictionary, thesaurus and encyclopedia. universal algebra. http://encyclopedia.thefreedictionary.com/Universal algebra

Dictionaries: General Computing Medical Legal Encyclopedia Universal algebra Word: Word Starts with Ends with Definition Universal algebra is the field of mathematics Mathematics is commonly defined as the study of patterns of structure, change, and space; more informally, one might say it is the study of 'figures and numbers'. In the formalist view, it is the investigation of axiomatically defined abstract structures using logic and mathematical notation; other views are described in Philosophy of mathematics. Mathematics might be seen as a simple extension of spoken and written languages, with an extremely precisely defined vocabulary and grammar, for the purpose of describing and exploring physical and conceptual relationships. Click the link for more information. that studies the ideas common to all algebraic structures In abstract algebra, an algebraic structure consists of a set together with one or more operations on the set which satisfy certain axioms. In case there are no ambiguities, we usually identify the set with the algebraic structure. For example, a group ( G ,*) is usually referred simply as a group G Depending on the operations and axioms, the algebraic structures get their names. The following is a partial list of algebraic structures:

32. Kernel (universal Algebra) - Encyclopedia Article About Kernel (universal Algebr encyclopedia article about Kernel (universal algebra). Kernel (universal algebra) in Free online English dictionary, thesaurus and encyclopedia. http://encyclopedia.thefreedictionary.com/Kernel (universal algebra)

Dictionaries: General Computing Medical Legal Encyclopedia Kernel (universal algebra) Word: Word Starts with Ends with Definition In the various branches of mathematics Mathematics is commonly defined as the study of patterns of structure, change, and space; more informally, one might say it is the study of 'figures and numbers'. In the formalist view, it is the investigation of axiomatically defined abstract structures using logic and mathematical notation; other views are described in Philosophy of mathematics. Mathematics might be seen as a simple extension of spoken and written languages, with an extremely precisely defined vocabulary and grammar, for the purpose of describing and exploring physical and conceptual relationships. Click the link for more information. that fall under the heading of abstract algebra Abstract algebra is the field of mathematics concerned with the study of algebraic structures such as groups, rings and fields. The term "abstract algebra" is used to distinguish the field from "elementary algebra" or "high school algebra" which teaches the correct rules for manipulating formulas and algebraic expressions involving real and complex numbers. Historically, algebraic structures usually arose first in some other field of mathematics, were specified axiomatically, and were then studied in their own right in abstract algebra. Because of this, abstract algebra has numerous fruitful connections to all other branches of mathematics.

33. 08: General Algebraic Systems However, the current meaning of the expression universal algebra dates from the work of Birkhoff and Ore in the 1930s. The appeal http://www.math.niu.edu/~rusin/known-math/index/08-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 08: General algebraic systems Introduction Here is an excerpt from the Math Reviews review of the book by Burris and Sankappanavar: For more information about this field, see that review (83k:08001) or 94d:08001. History Applications and related fields "Algebra" is a very broad section of mathematics; there are separate index pages here for specific algebraic categories (groups, fields, etc.) This heading focuses both on the broad principles covering all of algebra and on specific algebraic constructs not included in those other areas. By extension (and somewhat inappropriately) we use it to house a few resources discussing many areas of algebra. Universal algebra is arguably more a topic in Logic (03C05) (Model Theory), hence there is significant overlap. For Boolean algebras and generalizations see Ordered algebraic structures (06E) For groupoids, semigroups, and other multiplicative sets see Group Theory (sections 20L, 20M, 20N).

34. UNIVERSAL ALGEBRA - Meaning And Definition Of The Word Search Dictionary universal algebra Dictionary Entry and Meaning. Computing Dictionary. Definition http://www.hyperdictionary.com/computing/universal algebra

English Dictionary Computer Dictionary Thesaurus Dream Dictionary ... Medical Dictionary Search Dictionary: UNIVERSAL ALGEBRA: Dictionary Entry and Meaning Computing Dictionary Definition: The model theory of first-order equational logic See Also: logic HOME ABOUT HYPERDICTIONARY

35. Universal Algebra - Wikipedia, The Free Encyclopedia PhatNav s Encyclopedia A Wikipedia . universal algebra. universal algebra is the field of mathematics that studies the ideas common to all algebraic systems. http://www.phatnav.com/wiki/wiki.phtml?title=Universal_algebra

36. Online Encyclopedia - Universal Algebra Encyclopedia Entry for universal algebra. universal algebra is the field of mathematics that studies the ideas common to all algebraic structures. http://www.yourencyclopedia.net/Universal_algebra.html

Encyclopedia Entry for Universal algebra Dictionary Definition of Universal algebra Universal algebra is the field of mathematics that studies the ideas common to all algebraic structures Table of contents showTocToggle("show","hide") 1 Basic idea 2 Examples 2.1 Groups 2.2 Modules ... 3 Further issues Basic idea From the point of view of universal algebra, an algebra is a set A together with a collection of operations on A . An n -ary operation on A is a function that takes n elements of A and returns a single element of A . Thus, a 0-ary operation (or nullary operation ) is simply an element of A , or a constant , often denoted by a letter like a . A 1-ary operation (or unary operation ) is simply a function from A to A , often denoted by a symbol placed in front of its argument, like ~ x . A 2-ary operation (or binary operation ) is often denoted by a symbol placed between its arguments, like x y . Operations of higher or unspecified arity are usually denoted by function symbols, with the arguments placed in parentheses and separated by commas, like f x y z ) or f x x n After the operations have been specified, the nature of the algebra can be further limited by

37. Universal Algebra Previous Univac Next Universal Asynchronous Receiver/Transmitter. universal algebra. logic The model theory of firstorder equational logic. (1997-02-25). http://burks.brighton.ac.uk/burks/foldoc/60/121.htm

The Free Online Dictionary of Computing ( http://foldoc.doc.ic.ac.uk/ dbh@doc.ic.ac.uk Previous: Univac Next: Universal Asynchronous Receiver/Transmitter Universal algebra logic first-order equational logic

38. Algebra --  Encyclopædia Britannica universal algebra. Algebra began as the manipulation of numbers, using the four operations of arithmetic addition, subtraction, multiplication and division. http://www.britannica.com/eb/article?eu=120652&tocid=76984&query=algebra

39. Algebra --  Encyclopædia Britannica The topological structure of Lie groups. Other aspects of homological algebra. universal algebra Fields; Rings; Categories; Homological algebra; universal algebra. http://www.britannica.com/eb/article?eu=120643

40. Constraints And Universal Algebra (ResearchIndex) In this paper we explore the links between constraint satisfaction problems and universal algebra. We show that a constraint satisfaction http://citeseer.ist.psu.edu/85.html

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