Carlos Ortiz Home Page

Career Highlights

• 2006 - present Associate Professor, Arcadia University
• 1997 - 2006 Assistant Professor, Arcadia University
• 1997 Ph.D., Mathematical Logic, University of Wisconsin-Madison
• 1992 M.A., Mathematics, University of Wisconsin-Madison
• 1989 BSc., Civil Engineering, Universidad de los Andes
• 1987 BSc., Mathematics, Universidad de los Andes

Research interests

Model Theory for Analysis.

A brief description of the Model Theory of Analytic Structures.

Some of my papers:

• My dissertation: Truth and Approximate Truth in metric Spaces.
1. In PDF format (approximately 140 pages).
• “Approximate Truth and Nonstandard Analysis” is a paper on the relations between nonstandard analysis and the notion of approximate truth. This paper appeared in the Methodes et Anlyse Non Standard, Cahiers du Centre de Logique, 9, Louvain-La-Neuve, Bruylant-Academia,1996.
1. In PDF format (approximately 26 pages).
• “An Omitting Types Theorem for Normed Spaces”, A paper that studies the existence of a powerful Omitting Types Theorem for the logic of approximate formulas in normed spaces. This paper appeared in the Annals of Pure and Applied Logic, 108 (2001).
1. In PDF format (approximately 30 pages).
• "Uniform Versions of Infinitary Properties in Banach Spaces", A paper that studies the following situation: Suppose that there is a statement P true in all the metric structures of a class, under which conditions do we know that the "uniform version" of this statement holds? And what is the "uniform version"? The answer is that this situation holds for a very large set of properties (namely, the ones that are expressible in an infinitary language L).  In this paper I also obtain a general recipe to obtain the “uniform” version of the formulas in the language L. This paper is to appear in the Annals of Pure and Applied Logic.
1. In PDF format (approximately 35 pages).

Finite Model Theory

Some of my papers:

• "Métodos del Análisis No-estandar en la Teoría de Modelos Finitos" is a paper with A. Arratia that studies the use of Nonstandard Analysis tools to obtain results in Finite Model Theory. This paper appeared in the Acta Científica Venezolana, vol 52, No. 2, 2001.
• “Approximating the Expressive Power of Logics in Finite Models”, is a paper with A. Arratia that studies approximations of well-known extensions of first order logic with built-in order and arithmetic predicates by weaker logics that are more tractable. This paper was published in the Lectures Notes in Computer Science (here is the SpringerLink to it).
1. In PDF format (approximately 17 pages).

• "Counting Proportions of Sets: Expressive Power with Almost Order", is another paper with A. Arratia that looks into some finite model logics with order that capture meaningful complexity classes. It is well known that the inclusion of the order makes the logic “hard” to study. Our idea was to weaken the order to an almost order and to study the expressive power of the logics thus obtained and their relationship with the logics with full order. This paper was published in the Lecture Notes in Computer Science (here is the SpringerLink to it).
1. In PDF format (approximately 12 pages).
• “Expressive Power and Complexity of a Logic with Quantifiers that Count Proportions of Sets”, is an exploration of the expressive power, in terms of complexity, of logics whose quantifiers count proportions of sets with respect to the cardinality of the universe. This paper was published in the Journal of Logic and Computation (Here is a link to the abstract at the Oxford Journals website).

Selected Publications:

Internationalizing the University Mathematics Curriculum, with P. Appelbaum, L. Friedler and N.
Wolff, Journal of Studies in International Education, 0 (2008).

Delta Hedging of Mortgage-Servicing Portfolios Under Gamma Constraints, with A. Zissu, The Journal
of Risk Finance, 9 (2008), 379-390.

Fixed Income Securities With A Zero Macauley Duration: Senior Life Settlements, with A. Zissu
and C. Stone, Applied Financial Letters, 4 (2008),205-207.

Expressive Power and Complexity of a Logic With Quantifers That Count Proportions of Sets, with A.
Arratia, Journal of Logic and Computation, 16 (2006), 817-840.

On a Syntactic Approximation to Logics That Capture Complexity Classes, with A. Arratia, ECCC:
Electronic Coloquium on Computational Complexity ISSN 1433-8092 (2006), TR06-014.

Counting Proportions of Sets: Expressive Power with Almost Order, with A. Arratia, LATIN 2006,
Lecture Notes in Computer Sciences ( J. R. Correa et al eds.) 3887 (2006), 105-117.

Approximating the Expressive Power of Logics Infinite Models, with A. Arratia, LATIN 2004: Theo-
retical Informatics (M. Farach-Colton, ed.) Lecture Notes in Computer Science 2976 (2004), 540-556.

Uniform Versions of Infnitary Properties in Banach Spaces, Annals of Pure and Applied Logic.
(Accepted for publication in annals of Pure and Applied Logic).

Metodos del Analisis No-Estandar en la Teoria de Modelos Finitos, Acta Cientifica Venezolana, 52
(2001), 2-4.

An Omitting Types Theorem for Normed Spaces, Annals of Pure and Applied Logic, 108 (2001),
279-294.

Approximate Truth and Nonstandard Analysis, Methodes et Analyse Non Standard, Cahiers du
Centre de Logique, 9 (1996), 25-55.