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      <PublisherName>ijesm</PublisherName>
      <JournalTitle>International Journal of Engineering, Science and</JournalTitle>
      <PISSN>I</PISSN>
      <EISSN>S</EISSN>
      <Volume-Issue>volume 15,issue 8</Volume-Issue>
      <PartNumber/>
      <IssueTopic>Multidisciplinary</IssueTopic>
      <IssueLanguage>English</IssueLanguage>
      <Season>August 2026</Season>
      <SpecialIssue>N</SpecialIssue>
      <SupplementaryIssue>N</SupplementaryIssue>
      <IssueOA>Y</IssueOA>
      <PubDate>
        <Year>-0001</Year>
        <Month>11</Month>
        <Day>30</Day>
      </PubDate>
      <ArticleType>Engineering, Science and Mathematics</ArticleType>
      <ArticleTitle>__ampersandsignldquo;NONSTANDARD MODEL AND ITS AXIOMATIC REPRESENTATION__ampersandsignrdquo;</ArticleTitle>
      <SubTitle/>
      <ArticleLanguage>English</ArticleLanguage>
      <ArticleOA>Y</ArticleOA>
      <FirstPage>44</FirstPage>
      <LastPage>44</LastPage>
      <AuthorList>
        <Author>
          <FirstName> BABAN KUMAR and Dr. Mukund Kumar</FirstName>
          <LastName>Singh</LastName>
          <AuthorLanguage>English</AuthorLanguage>
          <Affiliation/>
          <CorrespondingAuthor>N</CorrespondingAuthor>
          <ORCID/>
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      <DOI/>
      <Abstract>Our main aim is to extend ZFC by replacing the regularity axiom to overcome the hurdle that every nonstandard theory has to deal with Hrback paradox. A. Robinson and E. Zakon initiated super structure approach to Nonstandard analyses. we show here that the Harback paradox may be dated in the universes of nonstandard set theory unlimited. The axiomatic theory *ZFC is an extension of the traditional framework of  set-theoretic strucre.</Abstract>
      <AbstractLanguage>English</AbstractLanguage>
      <Keywords/>
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        <Abstract>https://www.ijesm.co.in/ubijournal-v1copy/journals/abstract.php?article_id=16348&amp;title=__ampersandsignldquo;NONSTANDARD MODEL AND ITS AXIOMATIC REPRESENTATION__ampersandsignrdquo;</Abstract>
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      <References>
        <ReferencesarticleTitle>References</ReferencesarticleTitle>
        <ReferencesfirstPage>16</ReferencesfirstPage>
        <ReferenceslastPage>19</ReferenceslastPage>
        <References/>
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