Products of Baire spaces

Products of Baire spaces
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by Paul E. Cohen PDF

Proc. Amer. Math. Soc. 55 (1976), 119-124 Request permission

Only the usual axioms of set theory are needed to prove the existence of a Baire space whose square is not a Baire space.

References

Paul J. Cohen, Set theory and the continuum hypothesis, W. A. Benjamin, Inc., New York-Amsterdam, 1966. MR 0232676
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
Thomas J. Jech, Trees, J. Symbolic Logic 36 (1971), 1–14. MR 284331, DOI 10.2307/2271510

A new construction of a nonconstructible

subset of

M. R. Krom, Cartesian products of metric Baire spaces, Proc. Amer. Math. Soc. 42 (1974), 588–594. MR 334138, DOI 10.1090/S0002-9939-1974-0334138-9
Dorothy Maharam, Set functions and Souslin’s hypothesis, Bull. Amer. Math. Soc. 54 (1948), 587–590. MR 24955, DOI 10.1090/S0002-9904-1948-09051-6
Edward Marczewski, Séparabilité et multiplication cartésienne des espaces topologiques, Fund. Math. 34 (1947), 127–143 (French). MR 21680, DOI 10.4064/fm-34-1-127-143
Edwin W. Miller, A note on Souslin’s problem, Amer. J. Math. 65 (1943), 673–678. MR 9615, DOI 10.2307/2371874
John C. Oxtoby, Cartesian products of Baire spaces, Fund. Math. 49 (1960/61), 157–166. MR 140638, DOI 10.4064/fm-49-2-157-166
J. R. Shoenfield, Unramified forcing, Axiomatic Set Theory (Proc. Sympos. Pure Math., Vol. XIII, Part I, Univ. California, Los Angeles, Calif., 1967) Amer. Math. Soc., Providence, R.I., 1971, pp. 357–381. MR 0280359
Robert M. Solovay, Real-valued measurable cardinals, Axiomatic set theory (Proc. Sympos. Pure Math., Vol. XIII, Part I, Univ. California, Los Angeles, Calif., 1967) Amer. Math. Soc., Providence, R.I., 1971, pp. 397–428. MR 0290961
R. M. Solovay and S. Tennenbaum, Iterated Cohen extensions and Souslin’s problem, Ann. of Math. (2) 94 (1971), 201–245. MR 294139, DOI 10.2307/1970860

Problème

1

An alternative to the continuum hypothesis and its uses in general topology

Gaisi Takeuti and Wilson M. Zaring, Axiomatic set theory, Graduate Texts in Mathematics, Vol. 8, Springer-Verlag, New York-Berlin, 1973. With a problem list by Paul E. Cohen. MR 0416914
S. Tennenbaum, Souslin’s problem, Proc. Nat. Acad. Sci. U.S.A. 59 (1968), 60–63. MR 224456, DOI 10.1073/pnas.59.1.60