Hao Wang's $\mathfrak S$ system/$\Sigma$ system: a "transfinite type" theory that avoids the Goedel's theorems.

Long ago, while I was reading a book ($*$) about the various way to build set theories (Zermelo-Freankel, Von Neumann–Bernays–Gödel, and type theories), I read about a variant of type theory with weird metalogics properties called Hao Wang's $\mathfrak S$ system, and presented for the first time in the year 1954.

The weird properties were something about his ability to avoid the Goedel's theorems.

Now I can't find that book anymore, and on internet I can't find nothing about this. Someone can explain me in easy words that theory's special properties and help me finding some free readings and introductions about?

Edit: The thory allowed the types of the variables to have transfinite value like $\omega$ and can be extended to even bigger ordinals.

Update 05-28-13 I remember the title of the chapter, and was about "Cumulative orders and cumulative types".

($*$)The book was Ettore Casari - Questioni di filosofia della matematica. Milan: Feltrinelli 1964

The following is a list of the papers written by Hao Wang on the topic and published on journals:

1) The Formalization of Mathematics, Journal of Symbolic Logic 19, 241-266;
2) Ordinals Number and Predicative Set Theories, Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 5, 216-239.

There is another paper that has the title "Some formal details on Predicative Set Theories" (3). Interestingly, all those papers can be found in the following Hao Wang's book:

• A Survey of Mathematical Logic, Amsterdam: North Holland, 1963.
  [Reprinted as Logic, Computers and Sets, New York: Chealsea, 1970]

In particular, we have that paper (1) (the introductory one and the most philosophical, with an interesting introduction on the method of mathematics) is on chapter XXIII [pp.559-584], paper (3) is on chapter XXIV [pp.585-623], and paper (2) is on chapter XXV [pp.624-651].

Last piece of information about a presentation of the theory, that is about introducing the constructive approach in mathematics, is this review by Mueller (unfortunately, the other two pages are not visible, but they can be easily downloaded with a JSTOR account).

For the sake of completeness, it is possible to find some information in the "Handbook of Philosophy of Mathematics" edited by Andrew Irvine in the part on Constructivism in Mathematics under the section Predicativsm [pp.333-337].

I hope it helps.

Wang's system is discussed in some detail in "Foundations of set theory" by Fraenkel, Bar-Hillel and Levy (in Studies in logic and foundations of mathematics, vol. 67, pp. 175--178). The reference is to the "The Formalization of Mathematics" paper cited by above by Kolmin.