Abstract property with public getter, define private setter in concrete class possible?

Unfortunately, you can't do exactly what you want. You can do this with interfaces though:

public interface IInterface {
    string MyProperty { get; }
}

public class Class : IInterface {
    public string MyProperty { get; set; }
}

The way I would do it is to have a separate SetProperty method in the concrete classes:

public abstract class AbstractClass {
    public abstract string Value { get; }
}

public class ConcreteClass : AbstractClass {

    private string m_Value;
    public override string Value {
        get { return m_Value; }
    }

    public void SetValue(string value) {
        m_Value = value;
    }
}

Found a solution: How to override a getter-only property with a setter in C#?

public abstract class A
{
    public abstract int X { get; }
}
public class B : A
{
    public override int X { get { return 0; } }
}
/*public class C : B  //won't compile: can't override with setter
{
    private int _x;
    public override int X { get { return _x; } set { _x = value; } }
}*/
public abstract class C : B  //abstract intermediate layer
{
    public sealed override int X { get { return this.XGetter; }  }
    protected abstract int XGetter { get; }
}
public class D : C  //does same thing, but will compile
{
    private int _x;
    protected sealed override int XGetter { get { return this.X; } }
    public new virtual int X { get { return this._x; } set { this._x = value; } }
}

D is now equivalent to a class inheriting from B while also being able to override in a setter.