Nonregular ultrafilters and large cardinals

Nonregular ultrafilters and large cardinals
HTML articles powered by AMS MathViewer

Trans. Amer. Math. Soc. 224 (1976), 61-73

DOI: https://doi.org/10.1090/S0002-9947-1976-0419236-X

PDF | Request permission

The relationship between the existence of nonregular ultrafilters and large cardinals in the constructible universe is studied.

References

Miroslav Benda and Jussi Ketonen, Regularity of ultrafilters, Israel J. Math. 17 (1974), 231–240. MR 396264, DOI 10.1007/BF02756872

Model theory

Some combinatorial principles of L

Keith J. Devlin, Some weak versions of large cardinal axioms, Ann. Math. Logic 5 (1972/73), 291–325. MR 363906, DOI 10.1016/0003-4843(73)90010-7

Ultrafilters over uncountable cardinals

H. Jerome Keisler, Limit ultrapowers, Trans. Amer. Math. Soc. 107 (1963), 382–408. MR 148547, DOI 10.1090/S0002-9947-1963-0148547-1
Jussi Ketonen, Strong compactness and other cardinal sins, Ann. Math. Logic 5 (1972/73), 47–76. MR 469768, DOI 10.1016/0003-4843(72)90018-6

Open problems in the theory of ultrafilters

Inaccessibility properties of cardinals

Kenneth Kunen, Some applications of iterated ultrapowers in set theory, Ann. Math. Logic 1 (1970), 179–227. MR 277346, DOI 10.1016/0003-4843(70)90013-6
Kenneth Kunen, Ultrafilters and independent sets, Trans. Amer. Math. Soc. 172 (1972), 299–306. MR 314619, DOI 10.1090/S0002-9947-1972-0314619-7
K. L. Prikry, Changing measurable into accessible cardinals, Dissertationes Math. (Rozprawy Mat.) 68 (1970), 55. MR 262075
Karel Prikry, On a problem of Gillman and Keisler, Ann. Math. Logic 2 (1970), no. 2, 179–187. MR 269513, DOI 10.1016/0003-4843(70)90010-0

On descendingly complete ultrafilters

Dana Scott, Measurable cardinals and constructible sets, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 9 (1961), 521–524. MR 143710
Jack H. Silver, Indecomposable ultrafilters and $0\#$, Proceedings of the Tarski Symposium (Proc. Sympos. Pure Math., Vol. XXV, Univ. California, Berkeley, Calif., 1971) Amer. Math. Soc., Providence, R.I., 1974, pp. 357–363. MR 0360276

Boolean-valued models for set theory

Robert M. Solovay, A nonconstructible $\Delta _3^1$ set of integers, Trans. Amer. Math. Soc. 127 (1967), 50–75. MR 211873, DOI 10.1090/S0002-9947-1967-0211873-5

An estimate of cardinality of a power

35

P. Vopěnka and K. Hrbáček, On strongly measurable cardinals, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 14 (1966), 587–591 (English, with Russian summary). MR 211872