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Forcing in admissible sets. (English. Russian original) Zbl 0781.03028
Algebra Logic 29, No. 6, 424-430 (1990); translation from Algebra Logika 29, No. 6, 648-658 (1990).
An admissible set is constructed by forcing. Using this set, the author proves that a countable admissible set $$\mathbb{A}$$ has no non-trivial admissible end-extension with the same urelements and ordinals iff $$\mathbb{A}=\text{HF}(X)$$ for a finite $$X$$.

##### MSC:
 03C70 Logic on admissible sets 03E40 Other aspects of forcing and Boolean-valued models
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##### References:
 [1] Yu. L. Ershov, ”On the generatability of admissible sets,” Algebra Logika,26, No. 5, 577–596 (1987). · Zbl 0648.03027 [2] M. Makkai, ”Admissible sets and infinite logic,” in: A Handbook of Mathematical Logic, North Holland, New York (1977). · Zbl 0376.02031 [3] J. Shenfield, Mathematical Logic [Russian translation], Nauka, Moscow (1975). [4] J. Barwise, Admissible Sets and Structures, Springer-Verlag, Berlin (1975). · Zbl 0316.02047 [5] P. J. Cohen, ”The independence of the continuum hypothesis, I and II,” Proc. Nat. Acad. Sci. USA.50, 1143–1148 (1963);51, 105–110 (1964). · Zbl 0192.04401
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