### Sammanfattning

model theory focusing on the framework of abstract

elementary classes. We discuss the role of syntax and semantics

and the motivation to generalize first order model theory to nonelementary

frameworks and illuminate the study with concrete examples

of classes of models.

This second part continues to study the question of catecoricity

transfer and counting the number of structures of certain cardinality.

We discuss more thoroughly the role of countable models,

search for a non-elementary counterpart for the concept of completeness

and present two examples: one example answers a question

asked by David Kueker and the other investigates models of

Peano Arithmetic and the relation of an elementary end-extension

in terms of an abstract elementary class.

Originalspråk | engelska |
---|---|

Tidskrift | Bulletin of Iranian Mathematical Society |

Volym | 39 |

Utgåva | 1 |

Sidor (från-till) | 27-48 |

Antal sidor | 22 |

ISSN | 1018-6301 |

Status | Publicerad - mar 2013 |

MoE-publikationstyp | A2 Granska artikel i en vetenskaplig tidskrift |

### Vetenskapsgrenar

- 111 Matematik

### Citera det här

}

*Bulletin of Iranian Mathematical Society*, vol. 39, nr. 1, s. 27-48.

**Beyond first order logic : From number of structures to structure of numbers: Part II.** / Baldwin, J.; Hyttinen, T.; Kesälä, M.

Forskningsoutput: Tidskriftsbidrag › Översiktsartikel › Vetenskaplig › Peer review

TY - JOUR

T1 - Beyond first order logic

T2 - From number of structures to structure of numbers: Part II

AU - Baldwin, J.

AU - Hyttinen, T.

AU - Kesälä, M.

PY - 2013/3

Y1 - 2013/3

N2 - We study the history and recent developments in nonelementary model theory focusing on the framework of abstract elementary classes. We discuss the role of syntax and semantics and the motivation to generalize first order model theory to nonelementary frameworks and illuminate the study with concrete examples of classes of models. This second part continues to study the question of catecoricity transfer and counting the number of structures of certain cardinality. We discuss more thoroughly the role of countable models, search for a non-elementary counterpart for the concept of completeness and present two examples: one example answers a question asked by David Kueker and the other investigates models of Peano Arithmetic and the relation of an elementary end-extension in terms of an abstract elementary class.

AB - We study the history and recent developments in nonelementary model theory focusing on the framework of abstract elementary classes. We discuss the role of syntax and semantics and the motivation to generalize first order model theory to nonelementary frameworks and illuminate the study with concrete examples of classes of models. This second part continues to study the question of catecoricity transfer and counting the number of structures of certain cardinality. We discuss more thoroughly the role of countable models, search for a non-elementary counterpart for the concept of completeness and present two examples: one example answers a question asked by David Kueker and the other investigates models of Peano Arithmetic and the relation of an elementary end-extension in terms of an abstract elementary class.

KW - 111 Mathematics

KW - mathematical logic

KW - Model theory

M3 - Review Article

VL - 39

SP - 27

EP - 48

JO - Bulletin of Iranian Mathematical Society

JF - Bulletin of Iranian Mathematical Society

SN - 1018-6301

IS - 1

ER -