Redaktion: K. Sigmund, G. Greschonig (Univ. Wien, Strudlhofgasse ...

94 Mathematische Logik, Theoretische Informatik
[1] D. Asperó, Bounded forcing axioms and the size of the continuum. Submitted.
[2] D. Asperó, The Bounded Martin’s Maximum, Erdös cardinals and ψAC. Submitted.
[3] J. Bagaria, Bounded forcing axioms as principles of generic absoluteness,
Archive for Mathematical Logic, vol. 39 (2000), 393–401.
[4] M. Foreman, M. Magidor, S. Shelah, Martin’s Maximum, saturated ideals,
and non-regular ultrafilters. Part I, Annals of Mathematics, vol. 127 (1988),
1–47.
[5] M. Goldstern, S. Shelah, The Bounded Proper Forcing Axiom, J. Symbolic
Logic, vol. 60 (1995), 58–73.
[6] H. Woodin, The axiom of Determinacy, Forcing Axioms, and the Nonstationary
ideal, De Gruyter Series in Logic and its Applications. Number 1.
Berlin, New York, 1999.
Reflections on Finite Model Theory
PHOKION G. KOLAITIS
Computer Science Department, Univ. of California, Santa Cruz
Finite model theory can be succinctly described as the study of logics on classes
of finite structures. It is an area of research in the interface between logic, combinatorics,
and computational complexity that has been steadily developing during
the past twenty five years. In this talk, we trace the early origins of finite model
theory, highlight some of the main results in this area, and conclude with certain
challenging open problems.
The Puzzle of Transfinite Integers
ENDRE KÖVESI
Reindorfgasse 37/9, 1150 Wien
Consider the base ten, arabic numerals: 3� 10 0 � 3� 10 1 � 3� 10 2 ��������� 3� 10 n � �����
also written as 333 ����� or ¯3. According to set theory the members of the above
series are each finite ones, and constitute a least infinite set (of the equinumerical
class ℵ0) together. So do nonterminating decimals (like: 0� ¯3). Obviously “¯3” is
a finite symbol, representing a class ℵ0 set of digits of the numeral “3”. We can
say:“¯3 is ℵ0 long - digit wise.” In this ℵ0 long chain of three-s, each digit has one
immediate neighbour. Since ¯3 actually exists according to theory, it has exactly
one first and exactly one last member (digit) at the “end of infinity”. Clearly, as an
individual ¯3 has one predecessor (the sum 2� 10 0 � 3� 10 1 � 3� 10 2 � ����� � 3� 10 n � ����� )
and one successor (the sum 4� 10 0 � 3� 10 1 � 3� 10 2 ��������� 3� 10 n � ����� ). It is a positive
whole number (¯3). (So are: 000 ����� , 111 ����� , 222 ����� , ����� , 999 ����� , 14142 ����� ,