Set Theory and the Continuum Hypothesis Paul J. Cohen
Publisher: Dover Publications

Does anyone have any insight into the tetration of 2 and Aleph_0 ? Thus we have a surprising result: the fundamentality of the mundane truths of set-theory requires the non-mundane continuum hypothesis to be determinate. Assuming ZFC (Zermelo-Fraenkel set theory with the Axiom of Choice), the continuum hypothesis proposes that 2^Aleph_0 = Aleph_1. Paul Cohen 2: The Continuum Hypothesis. [This is a sequel to my post on the Axiom of Choice]. Cohen, Set Theory and the Continuum Hypothesis. Paul Cohen's Set Theory and the Continuum Hypothesis is a good reference in the subject, there is also a nice introduction in mathematical logic (first-order logic, Godel's theorems.). (From My interaction with Kurt Godel, reprinted in Cohen's Set Theory and the Continuum Hypothesis.) I still had a feeling of skepticism about Godel's work, but skepticism mixed with awe and admiration. This conjecture is now known as the Continuum Hypothesis (CH), but logicians in the 20th century proved that it is a statement independent of set theory. In the late 19th century, Georg Cantor's work in set theory opened up an exciting world: that of infinite numbers. Now, first, the "sometimes said to be," is an odd locution. [4] For a brief but rigorous account of the situation, see Paul J. Go any smaller, and you're good old mundane finite. Best4you12: Set Theory and the Continuum Hypothesis by Paul J. Not just Geometry, even in Set Theory it has been proven that we can make two diagrammatically opposite assumptions and still retain an internally consistent world. It should appear somewhere in the list. Taking Cohen's work together with Gödel's, they'd proved that one can neither prove nor disprove the continuum hypothesis, using the standard (most widely-accepted) rules of set theory. The idea will be important in theological matters to come.