Some combinatorial theorems equivalent to the prime ideal theorem

Cowen, R. H.

doi:10.1090/S0002-9939-1973-0319769-3

Some combinatorial theorems equivalent to the prime ideal theorem
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Proc. Amer. Math. Soc. 41 (1973), 268-273 Request permission

Abstract:

Some useful combinatorial selection lemmas are shown to be directly equivalent to the prime ideal theorem for boolean algebras.

References

Robert H. Cowen, A new proof of the compactness theorem for propositional logic, Notre Dame J. Formal Logic 11 (1970), 79–80. MR 278898
R. H. Cowen, A short proof of Rado’s lemma, J. Combinatorial Theory Ser. B 12 (1972), 299–300. MR 297581, DOI 10.1016/0095-8956(72)90043-3
N. G. de Bruijn and P. Erdös, A colour problem for infinite graphs and a problem in the theory of relations, Nederl. Akad. Wetensch. Proc. Ser. A. 54 = Indagationes Math. 13 (1951), 369–373. MR 0046630
E. S. Wolk, On theorems of Tychonoff, Alexander, and R. Rado, Proc. Amer. Math. Soc. 18 (1967), 113–115. MR 203680, DOI 10.1090/S0002-9939-1967-0203680-X
John L. Kelley, General topology, D. Van Nostrand Co., Inc., Toronto-New York-London, 1955. MR 0070144
J. Łoś and C. Ryll-Nardzewski, Effectiveness of the representation theory for Boolean algebras, Fund. Math. 41 (1954), 49–56. MR 65527, DOI 10.4064/fm-41-1-49-56
Elliott Mendelson, Introduction to mathematical logic, D. Van Nostrand Co., Inc., Princeton, N.J., 1964. MR 0164867
Jan Mycielski, Two remarks on Tychonoff’s product theorem, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 12 (1964), 439–441. MR 215731
Abraham Robinson, Introduction to model theory and to the metamathematics of algebra, North-Holland Publishing Co., Amsterdam, 1963. MR 0153570
R. Rado, Axiomatic treatment of rank in infinite sets, Canad. J. Math. 1 (1949), 337–343. MR 31993, DOI 10.4153/cjm-1949-031-1
Richard Rado, A selection lemma, J. Combinatorial Theory Ser. A 10 (1971), 176–177. MR 270920, DOI 10.1016/0097-3165(71)90021-5
E. S. Wolk, On theorems of Tychonoff, Alexander, and R. Rado, Proc. Amer. Math. Soc. 18 (1967), 113–115. MR 203680, DOI 10.1090/S0002-9939-1967-0203680-X