Abstract
It is the purpose of this article to explain briefly some concepts and methods, especially so called the theory of semites, which are studied in Prague seminar. The authors of the theory of semisets are P. Vopénka and P. Hájek. We present here some results (not in the most general form) that are contained in their book “Sets, Semisets, Models” (to be published) with their kind permission. This article was written as material to our lecture that was held in the Summer Institute in Varenna (Italy) and contains no our new results.
At first we give the following illustration in order to acquire some idea about semisets. The reader is already acquainted with the Gö el-Bernays' set theory (GB) from the lecture of prof. Mostowski (in what follows we shall denote this lecture by [M]) where also the universal class V and the class L of all constructible sets were defined.
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Literature
K. GÖDEL, The consistency of the axiom of choice, Princeton Univ. Press, 1940.
P.J. COHEN, The independence of the continuum hypothesis I, II, Proc. Nat. Acad. Sci. USA, 50(1963), 51(1964).
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Balcar, B. (2010). The General Theory of Semisets. In: Casari, E. (eds) Aspects of Mathematical Logic. C.I.M.E. Summer Schools, vol 48. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11080-1_5
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DOI: https://doi.org/10.1007/978-3-642-11080-1_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11078-8
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