Last edited by Aram
Sunday, May 17, 2020 | History

3 edition of Changing measurable into accessible cardinals found in the catalog.

Changing measurable into accessible cardinals

K. L. Prikry

Changing measurable into accessible cardinals

by K. L. Prikry

  • 34 Want to read
  • 30 Currently reading

Published by Państwowe Wydawnictwo Naukowe in Warszawa .
Written in English

    Subjects:
  • Set theory,
  • Transfinite numbers

  • Edition Notes

    Bibliography: p. [51]-52.

    StatementK.L. Prikry.
    SeriesDissertationes Mathematicae -- 68, Rozprawy matematyczne -- 68.
    The Physical Object
    Pagination55 p. ;
    Number of Pages55
    ID Numbers
    Open LibraryOL13627270M
    OCLC/WorldCa2334187

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Changing measurable into accessible cardinals by K. L. Prikry Download PDF EPUB FB2

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If you have a disability and are having trouble accessing information on this website or need materials in an alternate format, contact [email protected] for [email protected] for Author: Mohammad Golshani.

CHANGING MEASURABLE INTO SMALL ACCESSIBLE CARDINALS MOHAMMAD GOLSHANI Abstract. We give a detailed proof of the properties of the usual Prikry type forcing notion for turning a measurable cardinal into @!. introduction In this short note, we present a proof of the following known result.

Theorem Assume GCH holds and is a measurable. [11] A. Levy and R. Solovay, Measurable cardinals and the continuum hypothesis, Israel Journal of Mathematics 5 (), pp.

[12] K. Prikry, Measurable cardinals and saturated ideals. Amer. K. Prikry [] Changing measurable into accessible cardinals, Dissertationes Mathematicae (Rozprawy Matematyczne) 68, 5– MathSciNet zbMATH Google Scholar [] On a problem of Gillman and Keisler, Annals by:   supercompact cardinals contains a measure-one set of measurable cardinals, Prikry, Changing measur able into accessible c ardinals, Dissertationes Math.

Rozprawy Mat. 68 (), The cardinal κ is said to be measurable if κ > ℵ 0 and there exists a κ-ultrafilter on any set of cardinality κ, or, equivalently, on κ itself.

Henceforth, we fix a measurable cardinal κ and a κ-ultrafilter U on κ. Now let V = 〈V, ∈〉 be the universe of sets and write V κ for the collection of all functions with domain Size: KB. ADVANCES IN MATHEMAT () Successors of Singular Cardinals and Measurability ARTHUR W.

APTER Department of Mathematics, Rutgers University, Newark, New Jersey It is shown, starting from a model in which x measurable cardinal, how to force and obtain a model in which the Axiom of Choice is false and in which the successor of a Cited by: 8. E.M. Kleinberg, A combinatorial property of measurable cardinals, Z.

Math. Logik Grundlag. Math. 20 () [11] E.M. Kleinberg and R.A. Shore, On large cardinals and partition relations, J. Symbolic Logic 36 () Some coloring properties [12] K. Prikry, Changing measurable into accessible cardinals, Diss.

Math. 68 ( Author: Pierre Matet. Pcf theory and Woodin cardinals. Changing measurable into accessible cardinals. Article. K.L. Prikry; is an "iterable" weasel with no measurable cardinals, then either L[E] has. Abstract. This chapter provides an introduction to the basic theory of inner models of set theory, without fine structure.

Section 1 begins with the basic theory of Gödel’s class L of constructible sets, with an emphasis on the condensation property, introduces sharps, and includes a brief discussion of the Dodd-Jensen core model.

The next two sections describe the extension of these Cited by: Measurable Cardinals The measure ν is σ-additive and is nontrivial since ν({α})=µ(X α)=0for each α ∈ contradicts the choice of κ as the least cardinal that carries ameasure.

(ii) The proof is similar. We define an ideal J on γ by: Z ∈J if and only if f−1(Z) ∈ induced ideal J is σ-complete and σ-saturated. Let {r i: i ∈I}be a collection of nonnegative. In mathematics, a measurable cardinal is a certain kind of large cardinal number.

In order to define the concept, one introduces a two-valued measure on a cardinal κ, or more generally on any a cardinal κ, it can be described as a subdivision of all of its subsets into large and small sets such that κ itself is large, ∅ and all singletons {α}, α ∈ κ are small, complements of.

The thing about measurable cardinals is that they have pretty much the easiest definition to understand, among all the “large” cardinals.

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