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Determinacy in the Mitchell models

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. ...

##
###
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. ...

##
###
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.,

doi:10.1016/0168-0072(93)90081-n
fatcat:izewemprtbcm3gozu2y4c4roia
*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 ...##
###
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

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. ...

##
###
Π12 Wadge degrees

1996
*
Annals of Pure and Applied Logic
*

Suppose that any two # sets are comparable

doi:10.1016/0168-0072(95)00011-9
fatcat:y3w2a5yfsfdbbdqzpaf63dd4o4
*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. ...##
###
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]

2012
*
Handbook of the History of Logic
*

Building on

doi:10.1016/b978-0-444-51621-3.50004-9
fatcat:rxofgx3z6nelvlyhmdybzlox6e
*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 ...
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