Inner model theory bibliography (under construction)

• The fine structure of the constructible hierarchy, Ann. Math. Logic 4 (1972) pp. 229-308.
• Measures of order zero, handwritten notes, 1988, available here
• Making Cardinals omega-cofinal, handwritten notes, available here
• The core model for non-overlapping extender sequences, handwritten notes, 1991
• A New Fine Structure, handwritten notes, 1997, available here
• Addendum to A New Fine Structure, handwritten notes, 1998, available here
• Corrections and Remarks, handwritten notes, 1999, available here
• More on Iterability, handwritten notes, 2000, available here
• T-Mice, handwritten notes, 2001, available here

K. Hauser

• The consistency strength of projective absoluteness, Ann. Pure Appl. Logic 74 (1995), pp. 245-295.

K. Hauser and G. Hjorth

• Strong cardinals in the core model, Ann. Pure Appl. Logic 83 (1997), pp. 165-198.

K. Hauser and R. Schindler

• Projective uniformization revisited, Ann. Pure Appl. Logic 103 (2000), pp. 109-153.

R. Ketchersid

• Towards AD_R from an \omega_1 -dense ideal plus CH, Ph.D. thesis, Berkeley 2000, available here

P.Koepke

• The short core model and its application, Ph.D. thesis, 1983

B. Löwe and J.R. Steel

• An introduction to core model theory, in: Cooper, Truss (eds.), Sets and proofs, Cambridge Univ. Press, Cambridge 1999, pp. 103-157.

T.Martin and J.R.Steel

• A proof of projective determinacy, Journal of the Americ. Math. Soc. 2 (1989), pp. 71-125
• Iteration trees, Journal of the Americ. Math. Soc. 7 (1994), pp. 1-73

W.Mitchell

• The core model for sequences of measures I, Math.Proc.Cambrigde Philos.Soc. 95 (1984), pp. 228-260
• The core model for sequences of measures II, typescript, 1984.
• The core model up to a Woodin cardinal, in: Prawitz et al. (eds.), Logic, Methodology, and Philosophy of science, Vol. IX, 1991.
• A Measurable Cardinal with a club set of inaccessibles from o(kappa)=kappa, to appear in Trans. AMS.
• An introduction to inner models and large cardinals, a chapter for the Handbook on Set Theory.
• The Covering Lemma, a chapter for the Handbook on Set Theory.
• A Gitik iteration with nearly Easton factoring, submitted to the Journal of Symbolic Logic, September 6 2001.
• One repeat point gives a closed unbounded ultrafilter on omega_1, preprint.
• A hypothesis related to the Mahlo property , preprint.

W.Mitchell and E. Schimmerling

• Covering without countable closure, Math.Research Letters 2 (1995), pp. 595-609

W.Mitchell, E. Schimmerling, and J.R. Steel

• The covering lemma up to a Woodin cardinal, Ann Pure Appl.Logic 84 (1997), pp. 219-255

W.Mitchell and R. Schindler

• A universal extender model without large cardinal in V, in preparation.

W.Mitchell and J.R. Steel

• Fine structure and iteration trees, Lecture Notes in Logic No. 3, Springer-Verlag 1994.

I.Neeman

• Inner models in the region of a Woodin limit of Woodin cardinals, Ann.Pure Appl.Logic 116 (2002), pp. 67-155.

I.Neeman and J.R. Steel

• A Weak Dodd-Jensen Lemma, Journal of Symbolic Logic , vol. 64, Sept. 1999, pp. 1285-1294.

M. Rudominer and J.R. Steel

• Inner models with wellorders in L(R), preliminary draft, available here.

E. Schimmerling

• Combinatorial principles in the core model for one Woodin cardinal, Ann. Pure Appl. Logic 74 (1995) 153-201.
• Combinatorial set theory and inner models, in C.A. Di Prisco, J.A. Larson, J. Bagaria and A.R.D. Mathias (eds.), Set theory, Techniques and Applications, Curacao 1995 and Barcelona 1996 Conferences, 207-212, Kluwer Acad. Publ., Dordrecht, 1998.
• Covering properties of core models, in S.B. Cooper and J.K. Truss (eds.), Sets and Proofs, 281-299, London Math. Soc. Lecture Note Ser. 258, Cambridge Univ. Press, Cambridge, 1999.
• A finite family weak square principle, J. Symbolic Logic 64 (1999) 1087-1110.
• The ABC's of mice, Bull. Symbolic Logic 7 (2001) 485-503.
• Woodin cardinals, Shelah cardinals, and the Mitchell-Steel core model, to appear in Proc. Amer. Math. Soc.

E. Schimmerling and J.R.Steel

• Fine structure for tame inner models, Journal of Symb. Logic 61 (1996), pp. 621-639.
• The maximality of the core model, Trans. Amer. Math. Soc. 351 (1999), no.8, pp. 3119-3141.

E. Schimmerling and H. Woodin

• The Jensen covering property, J. Symbolic Logic 66 (2001) 1505-1523.

E. Schimmerling and M. Zeman

• Square in core models, Bull. Symbolic Logic 7 (2001) pp. 305-314
• A characterization of square in core models, Journal Math. Logic, submitted.

R.Schindler

• The core model up to one strong cardinal, Bonner Mathematische Schriften Nr. 295 (1997).
• Weak Covering at Large Cardinals, Mathematical Logic Quarterly 43 (1997), pp. 22-28.
• On a Chang Conjecture, Israel J. Math. 99 (1997), pp. 221-230.
• On a Chang Conjecture II, Archive for Mathematical Logic 37 (1998), pp. 215-220.
• Successive weakly compact or singular cardinals, Journal of Symb. Logic 64 (1999), pp. 139-146.
• Weak covering and the tree property, Archive for Mathematatical Logic 38 (1999), pp. 515-520.
• Coding into K by reasonable forcing, Trans. Amer.Math.Soc. 353 (2000), pp. 479-489
• Strong cardinals and sets of reals in L_{\omega_1}(R), Mathematical Logic Quarterly 45 (1999), pp. 361-369.
• The core model for almost linear iterations, Ann.Pure Appl.Logic 116 (2002), pp. 205-272.
• Iterates of the core model, Journal of Symbolic Logic, submitted.
• Mutual stationarity in the core model, Proc. LC 2001, submitted.
• Forcing axioms and projective sets of reals, Proc. FotFS III, submitted.
• A simple proof of \Sigma^1_3 correctness of K, preprint.
• Sharps and the \Sigma^1_3 correctness of K, preprint.

R.Schindler and J.R. Steel

• The strength of AD, preprint.

R.Schindler, J.R. Steel, and M. Zeman

• Deconstructing inner model theory, J. Symb. Logic, to appear.

J.R. Steel

• Inner models with many Woodin cardinals, Ann. Pure Appl. Logic 65 (1993), pp. 185-209.
• The well-foundedness of the Mitchell order, J. Symb. Logic 58 (1993), p. 931.
• Projectively well-ordered inner models, Ann. Pure Appl. Logic 74 (1995), no. 1, pp. 77-104.
• The core model iterability problem, Lecture Notes in Logic 8 (1996)
• An outline of inner model theory, available here
• Core models with more Woodin cardinals, available here
• A Theorem of Woodin on Mouse Sets, unpublished notes, available here.
• Woodin's Analysis of HOD L(R), unpublished notes, available here.

J.R. Steel and P.D. Welch

• \Sigma^1_3 absoluteness and the second uniform indiscernible, Israel J. Math. 104 (1998), 157--190.

W.H. Woodin

• The axiom of determinacy, forcing axioms, and the nonstationary ideal, Logic and Its Applications, vol. 1, de Gruyter, Berlin, 1999.
• The Continuum Hypothesis and the Omega Conjecture, available here
• Strong Axioms: Determinacy and Large Cardinals, available here
• Extender Sequences and beyond, available here

M. Zeman

• Inner models and large cardinals, Logic and Its Applications, vol. 5, de Gruyter, Berlin, 2002.

A.S. Zoble

• Stationary reflection and the determinacy of inductive games, Ph.D. thesis, Berkeley 2000, available here