Atlas home ||
Conferences |
Abstracts |
about Atlas
Conference in Algebra (in honour of the 70th birthday of Ervin Fried)
August 17-21, 1999
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences
Budapest, Hungary |
|
Organizers
László Márki
View Abstracts
Conference Homepage |
On a stronger version of the finitization problem
by
Tarek Sayed Ahmed
Mathematical Institute, Budapest, Hungary
We investigate a stronger version of the Finitization problem in Algebraic
Logic. We search for an algebraization of first order logic such that the
corresponding quasi-variety K of representable algebras is not only
finitely axiomatizable but also enjoys other (positive) properties such as:
-
(1)
-
K has the strong amalgamation property.
Assuming that K has a boolean reduct,
-
(2)
-
Every atomic algebra in K is completely representable.
(Has a representation that preserves infinite meets, whenever they exist.)
At the logical side, this corresponds to asking whether it is possible to
modify first order logic, in order to obtain a new logic L which is
not only (strongly) complete but also enjoys the following (positive)
properties:
-
(1)
-
The well-known theorems of of Beth, Craig and Robinson are valid in
L.
-
(2)
- L enjoys (some version of) Henkin-Orey's omitting types theorem.
Surprisingly, most well known solutions of versions of the weaker
``classical'' Finitization problem, are also solutions to the (corresponding
version of the) stronger problem.
We try to explain why.
Date received: August 5, 1999
Copyright © 1999 by the author(s).
The author(s) of this document and the organizers of the conference
have granted their consent to include this abstract in
Atlas Conferences Inc.
Document # cadj-25.