- Outer model satisfiability, submitted
- Cofinality
Changes Required for a Large
Set of Unapproachable Ordinals Below $\aleph_{\omega+1}$ ,
*Proceedings of the AMS,*135 (2007). - Cocovering and set forcing,
in
*Logic Colloquium `03*(Helsinki), eds. Stoltenberg-Hansen and Vaananen, A.K. Peters (2006), pp 345--376. - Forcing closed unbounded subsets of~$\aleph_{\omega_{1}+1}$, submitted.
- Outer models and
genericity,
*Journal of Symbolic Logic*, vol. 68, no. 2, June 2003, pp.389--418. - Forcing closed unbounded
subsets
of~$\omega_{2}$,
*Journal of Pure and Applied Logic*, vol. 110, 2001, pp.23--87. - Forcing closed
unbounded subsets
of~$\aleph_{\omega+1}$, in
*Sets and Proofs*, Lon. Math. Soc. Lec. Note Ser. (258), Eds, S.B. Cooper and J.K. Truss, Camb. Univ. Pr., 1999, pp.365--382. - Invisible
Genericity and $0^{\#}$,
*Journal of Symbolic Logic*, vol.63, no.4, December, 1998, pp.1297--1318. - A Non-generic Real
Incompatible with
$0^{\#}$,
*The Annals of Pure and Applied Logic*, vol.85, 1997, pp.156--192. - A Cardinal Preserving
Immune Partition of
the Ordinals,
*Fundamenta Mathematicae*, vol.148, 1995, pp.99--221.

- Outer model
satisfiability, UC Berkeley Logic Colloquium, May
2008

Slides *The branch problem*, UCLA Logic Colloquium, May 2004.

Abstract; Notes*Cofinalities and approachable ordinals below aleph_{omega+1}*, AMS Special Session on Set Theory, Phoenix, January 2004.

Abstract; Slides;*Outer models and genericity*, Logic Colloquium 2003, Helsinki, August 2003.

Abstract; Slides

- Coding a generic extension
of $L$
This 21 page manuscript gives a detailed proof from scratch of Jensen's famous theorem that there exist reals that are class generic but not set generic over $L$. The main simplification to Jensen coding is to use limit coding that is a variation on Jensen-Solovay successor coding. Some of the coding ideas from this paper are used in "A non-generic real incompatible with 0#". The manuscript incorporates several helpful comments by R.Solovay and David Cook.

- Notes on a theorem of Silver
This 7 page manuscript gives a proof of Silver's theorem (from a supercompact) that the GCH can fail at a measurable cardinal kappa. Rather than using a backwards Easton support iteration, it adds a kappa-tree with kappa++ many branches with (forward) Easton support condtions.

- An application of strong
covering
Let P(eta) denote the following proposition: There exists a regular uncountable cardinal kappa and sets of ordinals C_delta, for delta less than eta, such that

- sup(C_delta) is a regular cardinal greater than kappa;
- C_delta is closed in sup(C_delta); and
- if alpha and alpha' are ordinals of cofinality kappa in C_delta and C_delta', respectively (where delta and delta' are distinct) then alpha and alpha' have different L-cofinalitites.

- If n is a natural number, then P(n) is consistent, relative to the consistency of ZFC.
- If P(omega), then 0# exists.
- If 0# exists, then P(eta) holds for all eta.