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Nonstandard Models of Arithmetic and Set Theory
 
Edited by: Ali Enayat American University, Washington, DC
Roman Kossak City University of New York, New York, NY
Nonstandard Models of Arithmetic and Set Theory
Softcover ISBN:  978-0-8218-3535-7
Product Code:  CONM/361
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7951-1
Product Code:  CONM/361.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-3535-7
eBook: ISBN:  978-0-8218-7951-1
Product Code:  CONM/361.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
Nonstandard Models of Arithmetic and Set Theory
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Nonstandard Models of Arithmetic and Set Theory
Edited by: Ali Enayat American University, Washington, DC
Roman Kossak City University of New York, New York, NY
Softcover ISBN:  978-0-8218-3535-7
Product Code:  CONM/361
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7951-1
Product Code:  CONM/361.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-3535-7
eBook ISBN:  978-0-8218-7951-1
Product Code:  CONM/361.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 3612004; 167 pp
    MSC: Primary 03; 26;

    This is the proceedings of the AMS special session on nonstandard models of arithmetic and set theory held at the Joint Mathematics Meetings in Baltimore (MD). The volume opens with an essay from Haim Gaifman that probes the concept of non-standardness in mathematics and provides a fascinating mix of historical and philosophical insights into the nature of nonstandard mathematical structures. In particular, Gaifman compares and contrasts the discovery of nonstandard models with other key mathematical innovations, such as the introduction of various number systems, the modern concept of function, and non-Euclidean geometries.

    Other articles in the book present results related to nonstandard models in arithmetic and set theory, including a survey of known results on the Turing upper bounds of arithmetic sets and functions. The volume is suitable for graduate students and research mathematicians interested in logic, especially model theory.

    Readership

    Graduate students and research mathematicians interested in logic, especially model theory.

  • Table of Contents
     
     
    • Articles
    • Haim Gaifman — Non-standard models in a broader perspective [ MR 2089273 ]
    • Paola D’Aquino and Julia F. Knight — Coding in $I\Delta _0$ [ MR 2089274 ]
    • Ali Enayat — Automorphisms, Mahlo cardinals, and NFU [ MR 2089275 ]
    • Thomas Forster — AC fails in the natural analogues of $V$ and $L$ that model the stratified fragment of ZF [ MR 2089276 ]
    • Harvey M. Friedman — Working with nonstandard models [ MR 2089277 ]
    • Karel Hrbacek — Internally iterated ultrapowers [ MR 2089278 ]
    • Renling Jin — On some questions of Hrbacek and Di Nasso [ MR 2089279 ]
    • Alex M. McAllister — Turing upper bounds of jump ideals and Scott sets [ MR 2089280 ]
    • James H. Schmerl — Diversity in substructures [ MR 2089281 ]
    • Amir A. Togha — Automorphisms of countable recursively saturated models of set theory [ MR 2089282 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 3612004; 167 pp
MSC: Primary 03; 26;

This is the proceedings of the AMS special session on nonstandard models of arithmetic and set theory held at the Joint Mathematics Meetings in Baltimore (MD). The volume opens with an essay from Haim Gaifman that probes the concept of non-standardness in mathematics and provides a fascinating mix of historical and philosophical insights into the nature of nonstandard mathematical structures. In particular, Gaifman compares and contrasts the discovery of nonstandard models with other key mathematical innovations, such as the introduction of various number systems, the modern concept of function, and non-Euclidean geometries.

Other articles in the book present results related to nonstandard models in arithmetic and set theory, including a survey of known results on the Turing upper bounds of arithmetic sets and functions. The volume is suitable for graduate students and research mathematicians interested in logic, especially model theory.

Readership

Graduate students and research mathematicians interested in logic, especially model theory.

  • Articles
  • Haim Gaifman — Non-standard models in a broader perspective [ MR 2089273 ]
  • Paola D’Aquino and Julia F. Knight — Coding in $I\Delta _0$ [ MR 2089274 ]
  • Ali Enayat — Automorphisms, Mahlo cardinals, and NFU [ MR 2089275 ]
  • Thomas Forster — AC fails in the natural analogues of $V$ and $L$ that model the stratified fragment of ZF [ MR 2089276 ]
  • Harvey M. Friedman — Working with nonstandard models [ MR 2089277 ]
  • Karel Hrbacek — Internally iterated ultrapowers [ MR 2089278 ]
  • Renling Jin — On some questions of Hrbacek and Di Nasso [ MR 2089279 ]
  • Alex M. McAllister — Turing upper bounds of jump ideals and Scott sets [ MR 2089280 ]
  • James H. Schmerl — Diversity in substructures [ MR 2089281 ]
  • Amir A. Togha — Automorphisms of countable recursively saturated models of set theory [ MR 2089282 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.