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On countable generalised \(\sigma\)-algebras with a new proof of Gödel’s completeness theorem. (English) Zbl 0045.15002


MSC:

03-XX Mathematical logic and foundations

Keywords:

logic
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References:

[1] G. Birkhoff: Lattice Theory. Am. Math. Soc. Coll. Publ. XXV. Sec. 1948. · Zbl 0033.10103
[2] K. Gödel: Die Vollständigkeit der Axiome des logischen Funktionenkalküls. Mh. Math. Ph. 37 (1930). · JFM 56.0046.04
[3] D. Hilbert W. Ackermann: Grundzüge der theoretischen Logik. Grundl. d. math. Wiss. XXVII Springer, Zw. A. 1938. · JFM 64.0026.05
[4] D. Hilbert P. Bernays: Grundlagen der Mathematik. Bd. II, Springer 1939. · Zbl 0020.19301
[5] L. Henkin: A proof of completeness for the first order functional calculus. J. Symb. L. 14, (1949), 159-166. · Zbl 0034.00602 · doi:10.2307/2267044
[6] H. L. Loomis: On the representation of \(\sigma\)-complete Boolean algebras. Bull. Am. Math. Soc. 53 (1947), 757-760. · Zbl 0033.01103 · doi:10.1090/S0002-9904-1947-08866-2
[7] H. Mac Neille: Extensions of partially ordered sets. Proc. Nat. Ac. USA, 22 (1936), 45-50. · Zbl 0013.24302 · doi:10.1073/pnas.22.1.45
[8] A. Mostowski: Logika matematyczna. Monografie mat., Warszawa, 1948.
[9] A. Mostowski: Abzählbare Boolesche Körper und ihre Anwendung in der Metamathematik. Fund. Math. 29 (1937), 34-53. · Zbl 0016.33704
[10] L. Rieger: On \(\aleph_ \xi\)-complete free Boolean Algebras. (With an application to logic.) · Zbl 0044.26103
[11] R. Sikorski: On the representation of Boolean algebras as fields of sets. Fund. Math. 35 (1948), 247-258. · Zbl 0035.01704
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