# Partition relations for cardinal numbers

@article{Erds1965PartitionRF, title={Partition relations for cardinal numbers}, author={P{\'e}ter Erdős and Andr{\'a}s Hajnal and Richard Rado}, journal={Acta Mathematica Academiae Scientiarum Hungarica}, year={1965}, volume={16}, pages={93-196} }

1. INTRODUCTION In this paper our main object is the study of relations between cardinal numbers which are written in the form a-(b o , b,,. . .) r or a-(b)C ~° or (b) (b o b,) Such relations were introduced in [3] and [1]. They are called I-relations, Ii-relations and III-relations respectively, and they will be defined in 3. 1, 3. 2 and 3. 3. In sections 18 and 19 we shall introduce certain generalizations of these relations. Our whole theory can be considered as having arisen out of the…

## 258 Citations

Weak partition relations

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The partition relation 1+x1)3 ,,, which was known to contradict the continuLlm hypothesis [1], is disproved without this hypothesis. For cardinals K>?) and 2>1, let P(K, A) be the following partition…

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