The phrase "a greater equality" is correct and usable in written English.
It can be used when discussing the concept of increasing fairness or balance among individuals or groups in various contexts, such as social, economic, or political discussions.
Example: "The new policy aims to promote a greater equality in access to education for all students, regardless of their background."
Alternatives: "an increased equality" or "enhanced equality".
However, I prefer to see it as a levelling of power, a greater equality.
If the aim is to increase mobility by creating a greater equality in relative mobility chances, what can be achieved through educational policy alone is limited – far more so than politicians find it convenient to suppose.
It was grounded in a populist gesture and an unapologetically progressive conviction: that public institutions can and should serve the communities they represent, and should seek to generate a greater equality among the citizenry.
If Blears had announced an initiative seeking to strengthen the voice of women in society to create a greater equality between men and women, that would be a commendable move.
"Tom and I had a chat about this: what we are agreed on is there has to be a greater equality of working conditions … Workers working alongside each other should have the same rights.
Supporters of the proposal say it would create a greater equality between the sexes within the Church.
Such is the unforced, naturalistic mood that Durkin has created here, it allows the film's big-name actors to move with a great equality within it.
The American Civil Liberties Union does not support vouchers for several reasons, but the suggestion that vouchers are a lifeline to students who need help the most and an avenue to greater equality calls for a response.
Education is a primary driver of creating a society with greater equality of opportunity.
But I think we're moving in a direction of greater equality and I think that's a good thing.
The president went on: "I think we're moving in a direction of greater equality and — and I think that's a good thing".
