John R. Steel: Online Preprints

• An Outline of Inner Model Theory, in ``Handbook of Set Theory'', to appear. postscript. or pdf.
• with Benedikt Loewe. An Introduction to Core Model Theory, in Sets and Proofs, Logic Colloquium 1997 , volume 1, London Mathematical Society Lecture Notes 258. Cambridge University Press, Cambridge, 1999. postscript.
• with Itay Neeman. A Weak Dodd-Jensen Lemma. Journal of Symbolic Logic , vol. 64, Sept. 1999, pp. 1285-1294. postscript.
• with Ernest Schimmerling. The Maximality of the Core Model. Trans. Amer. Math. Soc. , vol. 351, pp. 3119-3141, 1999. postscript.
• with William Mitchell and Ernest Schimmerling. The Weak Covering Lemma up to a Woodin Cardinal, Annals of Pure and Applied Logic , vol. 84, pp. 219-255, 1997. postscript.
• Mathematics needs new axioms, to appear in Bulletin of Symbolic Logic . postscript.
• with Alessandro Andretta and Itay Neeman. The domestic levels of $K^c$ are iterable, Israel Journal of Mathematics , to appear. postscript.
• with Mitchell Rudominer. Inner models with wellorders in L(R), preliminary draft. postscript.
• with Ralf Schindler and Martin Zeman. Deconstructing inner model theory, Journal of Symbolic Logic, v. 67, June 2002, pp. 721-736. postscript.
• with Philip Welch. $ \Sigma_1^3$ correctness and the second uniform indiscernible, Israel Journal of Mathematics , {\bf 104 }, 1998, 157-190. postscript.
• A Theorem of Woodin on Mouse Sets, unpublished notes. postscript. or pdf.
• Woodin's Analysis of HOD ^L(R), unpublished notes. postscript.
• Core models with more Woodin cardinals, Journal of Symbolic Logic, v. 67, Sept. 2002, pp. 1197-1226. postscript.
• The derived model theorem, unpublished notes postscript.
• with Oliver Deiser. Iterations with long extenders, unpublished notes postscript.
• with D.A. Martin. The tree of a Moschovakis scale is homogeneous, to appear in a re-issue of the Cabal volumes postscript.
• Scales in K(R), to appear in a re-issue of the Cabal volumes postscript. or pdf.
• PFA implies AD^L(R) (Revised June 2005.) postscript. or pdf.
• Scales at the end of a weak gap (revised July 2007), postcript or pdf.
• Local K-c-constructions, postcript.
• Set Theory, (expository article for Encyclopedia of living support systems) postscript.
• Distinct iterable branches, postscript.
• Games and Scales, (expository article for The New Cabal ) pdf. or postscript.
• A stationary-tower-free proof of the derived model theorem, pdf. or postscript.
• The length $\omega_1$ open game quantifier propagates scales, pdf. or postscript.
• with Itay Neeman. Counterexamples to UBH and CBH, Journal of Symbolic Logic , Dec. 2005. pdf.
• with Ralf Schindler. The self-iterability of $L[\vec E]$, preliminary draft Feb. 2007. pdf.
• Derived models associated to mice, to appear, last revised July 15, 2007. pdf. or postscript.
• with Stuart Zoble. Determinacy from strong reflection. (Revised Nov. 2012.) pdf
• Godel's program. To appear in "Interpreting Godel", Juliette Kennedy editor, Cambridge University Press. pdf
• with Ronald Jensen. $K$ without the measurable, to appear in the Journal of Symbolic Logic. pdf
• with Nam Trang. $\mbox{{\sf AD}}^+$,derived models, and $\Sigma_1$ reflection. Notes for the 2010 Muenster workshop on hod mice and the core model induction. pdf
• with Itay Neeman. Equiconsistencies at subcompact cardinals. (October 2013 version.) To appear in AMS volume honoring Rich Laver. pdf
• with Itay Neeman. Plus-one premice. (Handwritten notes for June 2014 AIM workshop.) pdf
• with Itay Neeman. Fine structure for plus-one premice. (Handwritten notes, Part 1 pdf and Part 2 pdf
• Remarks on a paper of Sargsyan (Handwritten notes from April 2013, revised January 2015.) pdf
• HOD mice below ${\sf LST}^-$. (Handwritten notes from October 2013, in three parts.) Part 1 pdf , part 2 pdf , part 3 pdf
• Remarks on a hod mouse construction (Handwritten notes from August 2014. Essentially, part 4 of "HOD mice below ${\sf LST}^-$".) pdf
• Normalizing iteration trees and comparing iteration strategies. (Posted April 2016, corrected version posted August 2016. Revised versions posted August 2017, Jan. 2018, and Aug. 2018. Significantly revised and expanded version posted Oct. 2019. Please see the next three items for some nontrivial repairs. The book draft after that incorporates an alternative version of those repairs.) pdf
• Some $\lambda$-errors in NITCIS.(May 2020. Corrects some errors in the paper immediately above.) pdf
• Embedding normalization for mouse pairs.(June 2020. Continuation of the immediately previous item.) pdf
• Some fine structure needed to normalize well. (August 2020. Continuation of the last two items.) pdf
• A comparison process for mouse pairs. (April 2022. Prepublication version of a book based on the last four items. To appear in Lecture Notes in Logic, ASL and CUP. (NB: The copy displayed on this website is a pre-publication copy only. The final, published version can be purchased through Cambridge University Press and other standard distribution channels. This prepublication copy is made available for personal use only and must not be sold or re-distributed.) pdf
• Local HOD computation.(Handwritten notes July 2016.) pdf
• LSA from least branch hod pairs.(Handwritten notes June 2016.) pdf
• Hod pair capturing and short tree strategies. (Handwritten notes October 2016.) pdf
• with Nam Trang. Condensation for mouse pairs. (Revised version, August 2023.) pdf
• Mouse pairs and Suslin cardinals. (Revised version of July 5, 2023.)pdf
• Notes on work of Jackson and Sargsyan.pdf
• The comparison lemma.( Mar. 2022. To appear.) pdf
• Generically invariant set theory. (April 2022. To appear in a volume in honor of Penelope Maddy.) pdf
• with Benjamin Siskind. Full normalization for mouse pairs. July 2022. pdf
• Notes on work of Gappo and Sargsyan. July 2023. pdf

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