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Extensions of filters and fields of sets (I)

Published online by Cambridge University Press:  09 April 2009

E. Grzegorek  and
B. Weglorz
E. Grzegorek
Affiliation:
Instytut Matematyczny, Polskiej Akademii Nauk, Wroclaw, Kopernika 18, Poland.
B. Weglorz
Affiliation:
Instytut Matematyczny, Polskiej Akademii Nauk, Wroclaw, Kopernika 18, Poland.
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Abstract

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We investigate the problem of the existence of filters with some properties. This leads to a solution of two problems of Ulam concerning σ-fields on the real line.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 25 , Issue 3 , May 1978 , pp. 275 - 290
Copyright
Copyright © Australian Mathematical Society 1978

References

Balcar, B. and Vopěnka, P. (1972), ‘On systems of almost disjoint sets’, Bull. Acad. Polon. Sci. Sér. sci. math. astr. et phys. 20, 421–424.Google Scholar
Erdös, P. (1943), ‘Some remarks on set theory’, Ann. of Math. 44, 643–646.CrossRefGoogle Scholar
Fodor, G. (1956), ‘Eine Bemerkung zur Theorie der regresiven Funktionen’, Acta. Sci. Math. (Szeged) 17, 139–142.Google Scholar
Marczewski, E. (1946), ‘Remarques sur l'equivalence des classes d'ensembles’, Ann. Soc. Pol. Math. 19, 228.Google Scholar
Martin, D. A. and Solovay, R. M. (1970), ‘Internal Cohen extensions’, Ann. Math. Logic 2, 143–178.Google Scholar
Oxtoby, J. C. (1971), Measure and Category (Springer, New York).Google Scholar
Prikry, K. (1974), ‘Ultrafilters and almost disjoint sets’, General Topology and Appl. 4, 269–282.Google Scholar
Sierpiński, W. (1928), ‘Sur une décomposition d'ensembles’, Monatshefte Math. Phys. 35, 239–242.CrossRefGoogle Scholar
Sierpiński, W. (1934), Hypothèse du Continuum (Monografie Matenatyczne, Vol. 4, WarszawaLwów, 1934).Google Scholar
Sierpiński, W. (1934a), ‘Sur la dualité entre la première catégorie et la mesure nulle’, Fund. Math. 22, 276–280.CrossRefGoogle Scholar
Sierpiński, W. (1938), ‘Sur la décomposition des ensembles en sous-ensembles presque disjoints’, Mathematica, Cluj, 14, 15–17.Google Scholar
Solovay, R. M. (1971), ‘Real-valued measurable cardinals’, Axiomatic Set Theory (A.M.S. Providence, R.I. 1971).Google Scholar
Ulam, S. M. (1930), ‘Zur Masstheorie in der allgemeinen Mengenlehre’, Fund. Math. 16, 140–150.Google Scholar
Ulam, S. M. (1935–1940), Scottish Book (typewritten pages, Lwów 1935–1940).Google Scholar
Ulam, S. M. (1960), A collection of mathematical problems (Interscience Publishers, Inc., New York).Google Scholar