Kolmogorov Complexity and Symmetric Relational Structures

@article{Fouch1998KolmogorovCA,
  title={Kolmogorov Complexity and Symmetric Relational Structures},
  author={Willem L. Fouch{\'e} and Petrus H. Potgieter},
  journal={J. Symb. Log.},
  year={1998},
  volume={63},
  pages={1083-1094}
}
We study partitions of Fraiss6 limits of classes of finite relational structures where the partitions are encoded by infinite binary strings which are random in the sense of Kolmogorov-Chaitin. ? 
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References

SHOWING 1-10 OF 25 REFERENCES
Descriptive Complexity and Reflective Properties of Combinatorial Configurations
We study the Ramsey theoretic properties of combinatorial configurations which are generated by infinite binary strings which are random in the sense of Kolmogorov-Chaitin. Introduction In this paper…
Laws in Logic and Combinatorics
This is a survey of logical results concerning random structures. A class of relational structures on which a (finitely additive) probability measure has been defined has a 0–1 law for a particular…
Identifying randomness given by high descriptive complexity
TLDR
Methods for identifying random phenomena which are logical consequences of the fact that almost all real numbers are of a high descriptive complexity enable us to find complexity-theoretic versions of classical results in the theory of random series.
Asymptotic enumeration of partial orders on a finite set
By considering special cases, the number Pn of partially ordered sets on a set of n elements is shown to be (1 + O(lIn))Qn, where Qn is the number of partially ordered sets in one of the special…
ALGORITHMS AND RANDOMNESS
CONTENTS Introduction 389 1. Algorithmic Definition of Randomness: Infinite Case 390 1.1. From finite chains to infinite sequences 390 1.2. Three properties of a random sequence 391 1.3. Typical…
Ramsey's Theorem and Recursion Theory
TLDR
It is shown that if P is such a recursive partition of [ N ] n, then H ( P ) contains a set which is Π n 0 in the arithmetical hierarchy, and it is proved that for each n ≥ 2 there is a recursive partitions P of [N ] n into two classes such that H (P ) contains no Σ n 0 set.
The Average Number of Linear Extensions of a Partial Order
TLDR
An asymptotic formula is given for (a) the average number of linear extensions of an n -element partial order and (b) the number of suborders of ann -element linear order.
Ramsey's Theorem does not Hold in Recursive Set Theory
On a Problem of Formal Logic
This paper is primarily concerned with a special case of one of the leading problems of mathematical logic, the problem of finding a regular procedure to determine the truth or falsity of any given…
Algorithmic Information Theory
This paper reviews algorithmic information theory, which is an attempt to apply information-theoretic and probabilistic ideas to recursive function theory. Typical concerns in this approach are, for…
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