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Projective planes of infinite but isolic order

Published online by Cambridge University Press:  12 March 2014

J. C. E. Dekker
J. C. E. Dekker*
Affiliation:
Rutgers, The State University, New Brunswick, New Jersey 08903
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Extract

The main purpose of this paper is to show how partial recursive functions and isols can be used to generalize the following three well-known theorems of combinatorial theory.

(I) For every finite projective plane Π there is a unique number n such that Π has exactly n 2 + n + 1 points and exactly n 2 + n + 1 lines.

(II) Every finite projective plane of order n can be coordinatized by a finite planar ternary ring of order n. Conversely, every finite planar ternary ring of order n coordinatizes a finite projective plane of order n.

(III) There exists a finite projective plane of order n if and only if there exist n − 1 mutually orthogonal Latin squares of order n.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 41 , Issue 2 , June 1976 , pp. 391 - 404
Copyright
Copyright © Association for Symbolic Logic 1976

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References

REFERENCES

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