# Descriptions and Computation of Ultrapowers in L(R)

### Description

The results from this dissertation are an exact computation of ultrapowers by measures on cardinals $\aleph\sb{n},\ n\in w$, in $L(\IR$), and a proof that ordinals in $L(\IR$) below $\delta\sbsp{5}{1}$ represented by descriptions and the identity function with respect to sequences of measures are cardinals. An introduction to the subject with the basic definitions and well known facts is presented in chapter I. In chapter II, we define a class of measures on the $\aleph\sb{n},\ n\in\omega$, in $L(\IR$) and derive a formula for an exact computation of the ultrapowers of cardinals by these measures. In chapter III, we give the definitions ... continued below

### Physical Description

v, 90 leaves : ill.

### Creation Information

Khafizov, Farid T. August 1995.

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• Khafizov, Farid T.

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### Description

The results from this dissertation are an exact computation of ultrapowers by measures on cardinals $\aleph\sb{n},\ n\in w$, in $L(\IR$), and a proof that ordinals in $L(\IR$) below $\delta\sbsp{5}{1}$ represented by descriptions and the identity function with respect to sequences of measures are cardinals. An introduction to the subject with the basic definitions and well known facts is presented in chapter I. In chapter II, we define a class of measures on the $\aleph\sb{n},\ n\in\omega$, in $L(\IR$) and derive a formula for an exact computation of the ultrapowers of cardinals by these measures. In chapter III, we give the definitions of descriptions and the lowering operator. Then we prove that ordinals represented by descriptions and the identity function are cardinals. This result combined with the fact that every cardinal $<\delta\sbsp{5}{1}$ in $L(\IR$) is represented by a description (J1), gives a characterization of cardinals in $L(\IR$) below \$\delta\sbsp{5}{1}. Concrete examples of formal computations are shown in chapter IV.

### Physical Description

v, 90 leaves : ill.

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#### UNT Theses and Dissertations

Theses and dissertations represent a wealth of scholarly and artistic content created by masters and doctoral students in the degree-seeking process. Some ETDs in this collection are restricted to use by the UNT community.

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• August 1995

### Added to The UNT Digital Library

• March 24, 2014, 8:07 p.m.

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• April 7, 2015, 11:58 a.m.

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Khafizov, Farid T. Descriptions and Computation of Ultrapowers in L(R), dissertation, August 1995; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc277867/: accessed December 12, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .