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Determinacy in the Mitchell models

John R. Steel
1982 Annals of Mathematical Logic  
In the papers [4] and [5] , Mitchell has made substantial progress on the fundamental probl,~m of finding inner models for large cardinal hypothese..  ...  Friedma,1 showed that 1, determinacy fails in the inner model M (for various Fat, d M) by means of games in which the players must produce approximations to M itself, the player producing the better approximation  ...  Let By Kechris' theorem, ~oz+ 1-HI determinacy is false in L [U] . Notice that the proof actually shows that ~o2+ 1-II~ determinacy is false in the core model K.  ... 
doi:10.1016/0003-4843(82)90017-1 fatcat:lj3jv7ywuvhfvprbrl4ei6ykwu

Page 7159 of Mathematical Reviews Vol. , Issue 95m [page]

1995 Mathematical Reviews  
The general form of inner model was to emerge in the work of Mitchell.  ...  (b) The main new idea for what is perhaps best possible in the direction of a covering theorem was provided by Mitchell in late 1990, and developed in 1992 by Mitchell, Schimmerling, and Steel.  ... 

Page 5796 of Mathematical Reviews Vol. , Issue 96j [page]

1996 Mathematical Reviews  
Mitchell and J. R.  ...  In the third section the author duly establishes his main theorem, using Steel’s work, his own refinement, and the work of Mitchell-Schimmerling-Steel.  ... 

European Mathematical Society

2006 Mitteilungen der DMV  
The principle of determinacy has been crucial to the study of definable sets of real numbers.  ...  This paper surveys some of the uses of determinacy, concentrating specifically on the connection between determinacy and large cardinals, and takes this connection further, to the level of games of length  ...  Mitchell [24] , [25] developed the framework for models with many measurable cardinals, still using linear iterations.  ... 
doi:10.1515/dmvm-2006-0090 fatcat:wxlbsh3nizcmxkfu2uipnmot6m

Page 1317 of Mathematical Reviews Vol. , Issue 85d [page]

1985 Mathematical Reviews  
Mitchell and J. Silver [Mitchell, Ann. Math.  ...  On the one hand, it is proved that M always has at least 2"° submodules, so in a model of ZFC in which 2*° = 2": the answer is yes.  ... 

Master Index to Volumes 51–60

1993 Annals of Pure and Applied Logic  
DuBOSE, D.A., Determinacy and the sharp function on the reals DuBOSE, D.A., Determinacy and the sharp function on the reals DuBOSE, D.A., Determinacy and extended sharp functions on the reals,  ...  , G., PFENNING, F. and SCEDROV, A., Uni- form proofs as a foundation for logic programming MITCHELL, J.C. and MOGGI, E., Kripke-style models for typed lambda calculus MITCHELL, J., see LINCOLN  ... 
doi:10.1016/0168-0072(93)90081-n fatcat:izewemprtbcm3gozu2y4c4roia

Page 3253 of Mathematical Reviews Vol. , Issue 96f [page]

1996 Mathematical Reviews  
axiom of determinacy as well as being as strong a hypothesis as can be presently accommodated in inner models.  ...  In a forthcoming paper Mitchell, Steel and the author have established a covering the- orem for Steel’s core model K up to a Woodin cardinal stating 961:03044 that (with a technical hypothesis giving “  ... 

Projective determinacy

D. A. Martin, J. R. Steel
1988 Proceedings of the National Academy of Sciences of the United States of America  
The ZFC (Zermelo-Fraenkel, with the axiom of choice) axi-Abbreviations: ZFC, Zermelo-Fraenkel, with the axiom of choice; PD, projective determinacy; AD, axiom of determinacy. 6582 The publication costs  ...  It is shown that projective determinacy follows from large cardinal axioms weaker than the assertion that supercompact cardinals exist.  ...  With the appearance in 1978 of Mitchell (5) (extending the work of Silver, Kunen, and Mitchell), the inner model program seemed on the verge of completing these tasks.  ... 
doi:10.1073/pnas.85.18.6582 pmid:16593978 pmcid:PMC282021 fatcat:nd4x5r73zzdmbjwspv4u3a2p2e

Π12 Wadge degrees

Greg Hjorth
1996 Annals of Pure and Applied Logic  
Suppose that any two # sets are comparable in the sense of Wadge degrees. Then every real has a dagger.  ...  This argument proceeds by using the Dodd-Jensen core model theory to show that Vx E ~"(~'33) along with, say, 10' implies the existence of a KIi norm of length u2.  ...  Acknowledgements Most of the results first appeared in my dissertation, and I wish to thank my advisor, Hugh Woodin, for his help and advice.  ... 
doi:10.1016/0168-0072(95)00011-9 fatcat:y3w2a5yfsfdbbdqzpaf63dd4o4

Page 3797 of Mathematical Reviews Vol. , Issue 2002F [page]

2002 Mathematical Reviews  
We show that under these assumptions there is an in- ner model of V2 with a measurable cardinal « of Mitchell order «**.  ...  the axiom of determinacy (AD) there, provides forcing extensions in which ZFC and a strong maximality principle hold.  ... 

Page 5264 of Mathematical Reviews Vol. , Issue 2001H [page]

2001 Mathematical Reviews  
The author shows how generic extensions of fine structural models in the sense of W. J. Mitchell and J. R.  ...  The Mitchell-Steel models are inner models of the form L{E] for large cardinals characterizable in terms of sequences of extenders, generalizations of ultrafilters, and these models have as cumulative  ... 

Page 750 of Mathematical Reviews Vol. 53, Issue 3 [page]

1977 Mathematical Reviews  
games; the equivalence of £,' determinacy to there being only countable many reals constructible from any real; determinacy of all G,* games in the Lévy-Solovay model [see R. M.  ...  ., 1957; MR 20 #264] in his solution of the determinacy problem for G,** games. Other announced results are: determinacy of £,!  ... 

Page 4137 of Mathematical Reviews Vol. , Issue 93h [page]

1993 Mathematical Reviews  
., XXV, Providence, RI, 1974; MR 52 #106], it follows that, in the model above, x is the smallest strongly compact cardinal. The author concludes the paper by using some results of S.  ...  4137 and 2" >x*+, he uses Radin forcing to produce a model in which K is supercompact and {6 € x: 6 is a singular strong limit cardinal violating GCH} is unbounded in x.  ... 

Page 1709 of Mathematical Reviews Vol. , Issue 84e [page]

1984 Mathematical Reviews  
Truss (Paisley) Steel, John R. 84e:03059 Determinacy in the Mitchell models. Ann. Math. Logic 22 (1982), no. 2, 109-125.  ...  This paper fine-tunes the theory by exhibiting upper bounds on the amount of determinacy possible in Mitchell’s models, L(U).  ... 

Large Cardinals with Forcing [chapter]

Akihiro Kanamori
2012 Handbook of the History of Logic  
Building on the previous work of Mitchell, Dodd and Jensen formulated coherent sequences of extenders, built inner models relative to such, and established GCH in these models.  ...  In the light of the Dodd-Jensen work, Mitchell in the later 1970s (cf. [1984 ) developed the core model K[U] for coherent sequences U of ultrafilters, which corresponds to his L[U] as K DJ does to L[U  ... 
doi:10.1016/b978-0-444-51621-3.50004-9 fatcat:rxofgx3z6nelvlyhmdybzlox6e
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