A note on countably generated complete Boolean algebras
Author: Thomas J. Jech
Abstract | References | Additional Information
Abstract: In this note, we construct (assuming the G.C.H.) a countably generated cardinal preserving complete Boolean algebra of cardinality .
[1] H. Gaifman, Infinite Boolean polynomials. I, Fund. Math. 54 (1964), 229–250. MR 0168503, https://doi.org/10.4064/fm-54-3-229-250
[2] A. W. Hales, On the non-existence of free complete Boolean algebras, Fund. Math. 54 (1964), 45–66. MR 0163863, https://doi.org/10.4064/fm-54-1-45-66
[3] Thomas J. Jech, Lectures in set theory, with particular emphasis on the method of forcing, Lecture Notes in Mathematics, Vol. 217, Springer-Verlag, Berlin-New York, 1971. MR 0321738
[4] R. B. Jensen and R. M. Solovay, Some applications of almost disjoint sets, Mathematical Logic and Foundations of Set Theory (Proc. Internat. Colloq., Jerusalem, 1968) North-Holland, Amsterdam, 1970, pp. 84–104. MR 0289291
[5] Saul A. Kripke, An extension of a theorem of Gaifman-Hales-Solovay, Fund. Math. 61 (1967), 29–32. MR 0220641, https://doi.org/10.4064/fm-61-1-29-32
[6] Robert M. Solovay, New proof of a theorem of Gaifman and Hales, Bull. Amer. Math. Soc. 72 (1966), 282–284. MR 0186598, https://doi.org/10.1090/S0002-9904-1966-11493-3
[7] P. Vopěnka and P. Hájek, Theory of semisets, North-Holland, Amsterdam, 1972.
H. Gaifman, Infinite Boolean polynomials. I, Fund Math. 54 (1964), 229-250; errata, ibid. 57 (1965), 117. MR 29 #5765; 31 #2179. MR 0168503 (29:5765)
A. W. Hales, On the non-existence of free complete Boolean algebras, Fund. Math. 54 (1964), 45-66. MR 29 #1162. MR 0163863 (29:1162)
T. J. Jech, Lectures in set theory, with particular emphasis on the method of forcing, Lecture Notes in Math., vol. 217, Springer-Verlag, Berlin and New York, 1971. MR 48 #105. MR 0321738 (48:105)
R. B. Jensen and R. M. Solovay, Some applications of almost disjoint sets, Mathematical Logic and Foundations of Set Theory (Proc. Internat. Colloq., Jerusalem, 1968), North-Holland, Amsterdam, 1970, pp. 84-104. MR #6482. MR 0289291 (44:6482)
S. A. Kripke, An extension of a theorem of Gaifman-Hales-Solovay, Fund. Math. 61 (1967), 29-32. MR 36 #3693. MR 0220641 (36:3693)
R. M Solovay, New proof of a theorem of Gaifman and Hales, Bull. Amer. Math. Soc. 72 (1966), 282-284. MR 32 #4057. MR 0186598 (32:4057)
P. Vopěnka and P. Hájek, Theory of semisets, North-Holland, Amsterdam, 1972.