Bulletin of the American Mathematical Society

MathSciNet review: 1567459
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Book Information:

Author: A. J. Dodd
Title: The core model
Additional book information: London Mathematical Society Lecture Notes Series No. 61, Cambridge Univ. Press, New York, New York, 1982, xxxviii + 229 pp., $24.95. ISBN 0-5212-8530-5.

Paul Cohen, The independence of the continuum hypothesis, Proc. Nat. Acad. Sci. U.S.A. 50 (1963), 1143–1148. MR 157890, DOI 10.1073/pnas.50.6.1143

Keith I. Devlin and R. B. Jensen, Marginalia to a theorem of Silver, $\vDash$ISILC Logic Conference (Proc. Internat. Summer Inst. and Logic Colloq., Kiel, 1974) Lecture Notes in Math., Vol. 499, Springer, Berlin, 1975, pp. 115–142. MR 0480036

A. Dodd and R. Jensen, The core model, Ann. Math. Logic 20 (1981), no. 1, 43–75. MR 611394, DOI 10.1016/0003-4843(81)90011-5

Tony Dodd and Ronald Jensen, The covering lemma for $K$, Ann. Math. Logic 22 (1982), no. 1, 1–30. MR 661475, DOI 10.1016/0003-4843(82)90013-4

Tony Dodd and Ronald Jensen, The covering lemma for $K$, Ann. Math. Logic 22 (1982), no. 1, 1–30. MR 661475, DOI 10.1016/0003-4843(82)90013-4

Haim Gaifman, Uniform extension operators for models and their applications, Sets, Models and Recursion Theory (Proc. Summer School Math. Logic and Tenth Logic Colloq., Leicester, 1965) North-Holland, Amsterdam, 1967, pp. 122–155. MR 0220586

[Gö] Kurt Gödel, The consistency of the axiom of choice and of the generalized continuum hypothesis, Proc. Nat. Acad. Sci. U.S.A. 24 (1938), 556-557.

[H] Ron Holzman, Jensen's covering lemma--an elementary proof, 1980 (manuscript).

R. Björn Jensen, The fine structure of the constructible hierarchy, Ann. Math. Logic 4 (1972), 229–308; erratum, ibid. 4 (1972), 443. With a section by Jack Silver. MR 309729, DOI 10.1016/0003-4843(72)90001-0

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

William J. Mitchell, Sets constructible from sequences of ultrafilters, J. Symbolic Logic 39 (1974), 57–66. MR 344123, DOI 10.2307/2272343

[M2] William Mitchell, The core model for sequences of measures, 1980 (typescript).

William Mitchell, Hypermeasurable cardinals, Logic Colloquium ’78 (Mons, 1978) Studies in Logic and the Foundations of Mathematics, vol. 97, North-Holland, Amsterdam-New York, 1979, pp. 303–316. MR 567676

Frederick Rowbottom, Some strong axioms of infinity incompatible with the axiom of constructibility, Ann. Math. Logic 3 (1971), no. 1, 1–44. MR 323572, DOI 10.1016/0003-4843(71)90009-X

Dana Scott, Measurable cardinals and constructible sets, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 9 (1961), 521–524. MR 143710

Jack Silver, The consistency of the $\textrm {GCH}$ with the existence of a measurable cardinal, 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. 391–395. MR 0278937

Jack H. Silver, Some applications of model theory in set theory, Ann. Math. Logic 3 (1971), no. 1, 45–110. MR 409188, DOI 10.1016/0003-4843(71)90010-6

Jack Silver, On the singular cardinals problem, Proceedings of the International Congress of Mathematicians (Vancouver, B. C., 1974) Canad. Math. Congress, Montreal, Que., 1975, pp. 265–268. MR 0429564

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

[U] Stanislaw Ulam, Zur masstheorie in der algemein Mengenlehre, Fund. Math. 16 (1930), 140-150.

[C] Paul Cohen, The independence of the continuum hypothesis, Proc. Nat. Acad. Sci. U.S.A. 50 (1963), 1143-1148; ibid. 51 (1964), 145-149. MR 0157890




[DeJ] Keith Devlin and Ronald Jensen, Marginalia to a theorem of Silver ISILC Logic Conference (Kiel, 1974), Lecture Notes in Math., vol. 499, Springer-Verlag, Berlin and New York, 1975, pp. 115-142. MR 480036




[DoJ1] Anthony Dodd and Ronald Jensen, The core model, Ann. Math. Logic 20 (1981), 43-75. MR 611394




[DoJ2] Anthony Dodd and Ronald Jensen, The covering lemma for K, Ann. Math. Logic 22 (1982), 1-30. MR 661475




[DoJ3] Anthony Dodd and Ronald Jensen, The covering lemma for L[U], Ann. Math. Logic 22 (1982), 127-135. MR 667224




[Ga] Haim Gaifman, Uniform extension operators for models and their applications, Sets, Models, and Recursion Theory, (J. Crossley, ed.), North-Holland, Amsterdam, 1967, pp. 122-155. MR 220586




[Gö] Kurt Gödel, The consistency of the axiom of choice and of the generalized continuum hypothesis, Proc. Nat. Acad. Sci. U.S.A. 24 (1938), 556-557.




[H] Ron Holzman, Jensen's covering lemma--an elementary proof, 1980 (manuscript).




[J] Ronald Jensen, The fine structure of the constructible hierarchy, Ann. Math. Logic 4 (1972), 229-308. MR 309729




[K] Kenneth Kunen, Some applications of iterated ultrapowers in set theory, Ann. Math. Logic 1 (1970), 179-227. MR 277346




[M1] William Mitchell, Sets constructible from sequences of ultrafilters, J. Symbolic Logic 39 (1974), 57-66. MR 344123




[M2] William Mitchell, The core model for sequences of measures, 1980 (typescript).




[M3] William Mitchell, Hypermeasurable cardinals Logic Colloquium 1978 (M. Boffa et al., eds.), North-Holland, Amsterdam, 1979, pp. 303-316. MR 567676




[R] Frederick Rowbottom, Some strong axioms of infinity incompatible with the axiom of constructibility, Ann. Math. Logic 3 (1971), 1-44. MR 323572




[Sc] Dana Scott, Measurable cardinals and constructible sets, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 9 (1961), 521-524. MR 143710




[Si1] Jack Silver, The consistency of the GCH with the existence of a measurable cardinal, Axiomatic Set Theory (D. Scott, ed.), Proc. Sympos. Pure Math., vol. 13, Amer. Math. Soc., Providence, R.I., 1971, pp. 391-396. MR 278937




[Si2] Jack Silver, Some applications of model theory in set theory, Ann. Math. Logic 3 (1971), 45-110. MR 409188




[Si3] Jack Silver, On the singular cardinals problem, Proc. Internat. Congress. Math., Vancouver, 1974, pp. 265-268. MR 429564




[So] Robert Solovay, A nonconstructible Δ¹₃ set of integers, Trans. Amer. Math. Soc. 127 (1967), 50-75. MR 211873




[U] Stanislaw Ulam, Zur masstheorie in der algemein Mengenlehre, Fund. Math. 16 (1930), 140-150.