Hi Jim!

You don´t say anything about where in Sweden your great grandfather is born.

I have tried to look in swedish sensus 1880 after a Carl Fredrik (often was Carl in Sweden changed to Charles in the US).

I found no one born in 1870 but one born in 1875 in Lövö (an island in the lake Mälaren) close to Stockholm, his fathers name was Anders Fredrik Blomberg. I also found one born in Stockholm town 1878, his fathers name was Johan Fredrik Blomberg.

I found none with the name Charles Fredrik and a father called Blomberg, but I found two kids with the name Charles Fredrik born 1870, but none of them had a father with the name Blomberg.

One was Charles Fredrik Hjalmar from Gotheborg, his father was Johan Fredrik Jansson

Another was Charles Fredrik born i Maria Magdalena in Stockholm, his father was Viktor Leonard von Bentzen

I don´t know if any of these kids could be your great grandfather.