Beyond first order logic

From number of structures to structure of numbers: Part II

Forskningsoutput: TidskriftsbidragÖversiktsartikelVetenskapligPeer review

Sammanfattning

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.
Originalspråkengelska
TidskriftBulletin of Iranian Mathematical Society
Volym39
Utgåva1
Sidor (från-till)27-48
Antal sidor22
ISSN1018-6301
StatusPublicerad - mar 2013
MoE-publikationstypA2 Granska artikel i en vetenskaplig tidskrift

Vetenskapsgrenar

  • 111 Matematik

Citera det här

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

I: Bulletin of Iranian Mathematical Society, Vol. 39, Nr. 1, 03.2013, s. 27-48.

Forskningsoutput: TidskriftsbidragÖversiktsartikelVetenskapligPeer 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 -