We prove that if the continuum hypothesis is assumed andkis a regular uncountable cardinal, then there is a valued field of cardinalitykand equicharacteristicpinto which every valued field of cardinality ≤kand equicharacteristicpcan be embedded. The same is true for a certain class of ordered valued fields. We prove a genreral existence theorem forηα-Structures which provides a simple uniform proof for the existence ofηα-Setsηα-groups, andηα-fields.