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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenFri, 12 Apr 2024 16:15:53 +0000The axiom of determinacy, strong partition properties and nonsingular measures
https://resolver.caltech.edu/CaltechAUTHORS:20130531-114321828
Authors: {'items': [{'id': 'Kechris-A-S', 'name': {'family': 'Kechris', 'given': 'Alexander S.'}}, {'id': 'Kleinberg-E-M', 'name': {'family': 'Kleinberg', 'given': 'Eugene M.'}}, {'id': 'Moschovakis-Y-N', 'name': {'family': 'Moschovakis', 'given': 'Yiannis N.'}}, {'id': 'Woodin-W-H', 'name': {'family': 'Woodin', 'given': 'W. Hugh'}}]}
Year: 1981
DOI: 10.1007/BFb0090236
In this paper we study the relationship between AD and strong partition properties of cardinals as well as some consequences of these properties themselves.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/hayep-6ny35Equivalence of partition properties and determinacy
https://resolver.caltech.edu/CaltechAUTHORS:KECpnas83
Authors: {'items': [{'id': 'Kechris-A-S', 'name': {'family': 'Kechris', 'given': 'Alexander S.'}}, {'id': 'Woodin-W-H', 'name': {'family': 'Woodin', 'given': 'W. Hugh'}}]}
Year: 1983
PMCID: PMC393690
It is shown that, within L(R), the smallest inner model of set theory containing the reals, the axiom of determinacy is equivalent to the existence of arbitrarily large cardinals below Θ with the strong partition property ĸ → (ĸ)^ĸ.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/6x4k8-ghn42Ranks of differentiable functions
https://resolver.caltech.edu/CaltechAUTHORS:20130528-145231519
Authors: {'items': [{'id': 'Kechris-A-S', 'name': {'family': 'Kechris', 'given': 'Alexander S.'}}, {'id': 'Woodin-W-H', 'name': {'family': 'Woodin', 'given': 'W. Hugh'}}]}
Year: 1986
DOI: 10.1112/S0025579300011244
The purpose of this paper is to define and study a natural rank function
which associates to each differentiable function (say on the interval [0, 1]) a
countable ordinal number, which measures the complexity of its derivative.
Functions with continuous derivatives have the smallest possible rank 1, a
function like x^2 sin (x^(-1)) has rank 2, etc., and we show that functions of any
given countable ordinal rank exist. This exhibits an underlying hierarchical
structure of the class of differentiable functions, consisting of ω_1 distinct levels.
The definition of rank is invariant under addition of constants, and so it
naturally assigns also to every derivative a unique rank, and an associated
hierarchy for the class of all derivatives.
The set D of functions in C[0, 1] which are everywhere differentiable is a
complete coanalytic (and thus non-Borel) set (Mazurkiewicz [Maz]; see Section
2 below) and it will tum out that the rank function we define has the
right descriptive set theoretic properties summarized in the concept of a
coanalytic norm, explained in Section 1.
Our original description of the rank function was in terms of wellfounded
trees and is given in Section 4. In Section 3 we give an equivalent description
in terms of a Cantor-Bendixson type analysis. We would like to acknowledge
here the contribution of D. Preiss. It was in a conversation with one of the
authors that this equivalent description was formulated.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/xaers-p8324The Structure of σ-Ideals of Compact Sets
https://resolver.caltech.edu/CaltechAUTHORS:20130522-103643006
Authors: {'items': [{'id': 'Kechris-A-S', 'name': {'family': 'Kechris', 'given': 'A. S.'}}, {'id': 'Louveau-A', 'name': {'family': 'Louveau', 'given': 'A.'}}, {'id': 'Woodin-W-H', 'name': {'family': 'Woodin', 'given': 'W. H.'}}]}
Year: 1987
DOI: 10.2307/2000338
Motivated by problems in certain areas of analysis, like measure theory and harmonic analysis, where σ-ideals of compact sets are encountered very often as notions of small or exceptional sets, we undertake in this paper a descriptive set theoretic study of σ-ideals of compact sets in compact metrizable spaces. In the first part we study the complexity of such ideals, showing that the structural condition of being a σ-ideal imposes severe definability
restrictions. A typical instance is the dichotomy theorem, which states that σ-ideals which are analytic or coanalytic must be actually either complete coanalytic or else G_δ. In the second part we discuss (generators or as we call
them here) bases for σ-ideals and in particular the problem of existence of Borel bases for coanalytic non-Borel σ-ideals. We derive here a criterion for the nonexistence of such bases which has several applications. Finally in the
third part we develop the connections of the definability properties of σ-ideals with other structural properties, like the countable chain condition, etc.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ymnan-6h009Supercompact cardinals, sets of reals, and weakly homogeneous trees
https://resolver.caltech.edu/CaltechAUTHORS:WOOpnas88
Authors: {'items': [{'id': 'Woodin-W-H', 'name': {'family': 'Woodin', 'given': 'W. Hugh'}}]}
Year: 1988
DOI: 10.1073/pnas.85.18.6587
PMCID: PMC282022
It is shown that if there exists a supercompact cardinal then every set of reals, which is an element of [Note: See the image of page 6587 for this formatted text] L(R), is the projection of a weakly homogeneous tree. As a consequence of this theorem and recent work of Martin and Steel [Martin, D. A. & Steel, J. R. (1988) Proc. Natl. Acad. Sci. USA 85, 6582-6586], it follows that (if there is a supercompact cardinal) every set of reals in [Note: See the image of page 6587 for this formatted text] L(R) is determined.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/yqbz6-5me42A strong boundedness theorem for dilators
https://resolver.caltech.edu/CaltechAUTHORS:20130517-105346791
Authors: {'items': [{'id': 'Kechris-A-S', 'name': {'family': 'Kechris', 'given': 'A. S.'}}, {'id': 'Woodin-W-H', 'name': {'family': 'Woodin', 'given': 'W. H.'}}]}
Year: 1991
DOI: 10.1016/0168-0072(91)90041-J
We prove a strong boundedness theorem for dilators: if A ⊆ DIL is Σ^1_1, then there is a recursive dilator D_0 such that ∀D ∈ A (D can be embedded into D_0).https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/3b1ft-4qg60The axiom of determinacy, strong partition properties, and nonsingular measures
https://resolver.caltech.edu/CaltechAUTHORS:20180810-141457603
Authors: {'items': [{'id': 'Kechris-A-S', 'name': {'family': 'Kechris', 'given': 'Alexander S.'}}, {'id': 'Kleinber-E-M', 'name': {'family': 'Kleinber', 'given': 'Eugene M.'}}, {'id': 'Moschovakis-Y-N', 'name': {'family': 'Moschovakis', 'given': 'Yiannis N.'}}, {'id': 'Woodin-W-H', 'name': {'family': 'Woodin', 'given': 'W. Hugh'}}]}
Year: 2008
DOI: 10.1017/CBO9780511546488.017
[no abstract]https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/6h1q9-t1a76The equivalence of partition properties and determinacy
https://resolver.caltech.edu/CaltechAUTHORS:20130731-151623397
Authors: {'items': [{'id': 'Kechris-A-S', 'name': {'family': 'Kechris', 'given': 'Alexander S.'}}, {'id': 'Woodin-W-H', 'name': {'family': 'Woodin', 'given': 'W. Hugh'}}]}
Year: 2008
This paper was circulated in handwritten form in March
1982 and contained Sections 1-4 below. There is an additional Section 5
containing information about the solution of a problem mentioned in the last
paragraph of Section I.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8kgpe-kdr68Generic codes for uncountable ordinals, partition properties, and elementary embeddings
https://resolver.caltech.edu/CaltechAUTHORS:20130731-150603194
Authors: {'items': [{'id': 'Kechris-A-S', 'name': {'family': 'Kechris', 'given': 'Alexander S.'}}, {'id': 'Woodin-W-H', 'name': {'family': 'Woodin', 'given': 'W. Hugh'}}]}
Year: 2008
This paper was circulated in handwritten form in December 1980 and contained Sections 1-7 below. There are two additionalSections 8 and 9 here that contain further material and comments.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/dbhn2-1d867