Automated property with getter only, can be set, why?

This is a new C# 6 feature, “Getter-only auto-properties”, also known as “Auto-Property Initializers for Read-Only Properties” as discussed in this MSDN magazine article ‘C# : The New and Improved C# 6.0’ by Mark Michaelis and in the C# 6.0 draft Language Specification.

The read-only field’s setter is only accessible in the constructor, in all other scenarios the field is still read only and behaves as before.

This is a convenience syntax to reduce the amount of code you need to type and to remove the need to explicitly declare a private module level variable to hold the value.

This feature was seen as important as, since the introduction of Auto-Implemented Properties in C#3, mutable properties (those with a getter and setter) had become quicker to write than immutable ones (those with only a getter), meaning people were being tempted to use mutable properties to avoid having to type the code for a backing field usually required for read-only properties. There is more discussion of Auto-Implemented properties in the relevant section of the Microsoft C# Programming Guide.

This blog post, ‘#1,207 – C# 6.0 – Auto-Property Initializers for Read-Only Properties’ by Sean Sexton Has a good explanation and example as follows:

Prior to C# 6.0, if you wanted a read-only (immutable) property, you’d
typically use a read-only backing field that is initialized in the
constructor, as shown below.

public class Dog 
{
    public string Name { get; set; }

    // DogCreationTime is immutable
    private readonly DateTime creTime;
    public DateTime DogCreationTime 
    {
        get { return creTime; }
    }

    public Dog(string name)
    {
        Name = name;
        creTime = DateTime.Now;
    }
}

In C# 6.0, you can use auto-implemented properties to implement a
read-only property. You do this by using an auto-property
initializer. The result is much cleaner than the above example, where
we had to explicitly declare a backing field.

public class Dog
{
    public string Name { get; set; }

    // DogCreationTime is immutable
    public DateTime DogCreationTime { get; } = DateTime.Now;

    public Dog(string name)
    {
        Name = name;
    }
}

More details can also be found in the dotnet Roslyn repo on GitHub:

Auto-properties can now be declared without a setter.

The backing field of a getter-only auto-property is implicitly
declared as readonly (though this matters only for reflection
purposes). It can be initialized through an initializer on the
property as in the example above. Also, a getter-only property can be
assigned to in the declaring type’s constructor body, which causes the
value to be assigned directly to the underlying field:

This is about expressing types more concisely, but note that it also
removes an important difference in the language between mutable and
immutable types: auto-properties were a shorthand available only if
you were willing to make your class mutable, and so the temptation to
default to that was great. Now, with getter-only auto-properties, the
playing field has been leveled between mutable and immutable.

and in the C# 6.0 draft Language Specification (NB: The language specification is final as far as Microsoft are concerned, but it is yet to be approved as a EMCA/ISO standard, hence the ‘draft’):

Automatically implemented properties

An automatically implemented property (or auto-property for short), is
a non-abstract non-extern property with semicolon-only accessor
bodies. Auto-properties must have a get accessor and can optionally
have a set accessor.

When a property is specified as an automatically implemented property,
a hidden backing field is automatically available for the property,
and the accessors are implemented to read from and write to that
backing field. If the auto-property has no set accessor, the backing
field is considered readonly (Readonly fields). Just like a readonly
field, a getter-only auto-property can also be assigned to in the body
of a constructor of the enclosing class. Such an assignment assigns
directly to the readonly backing field of the property.

An auto-property may optionally have a property_initializer, which is
applied directly to the backing field as a variable_initializer
(Variable initializers).