Archive for Mathematical Logic 47 (5):447-464 (2008)

Authors
Ali Enayat
University of Gothenburg
Abstract
This paper develops the model theory of ordered structures that satisfy Keisler’s regularity scheme and its strengthening REF ${(\mathcal{L})}$ (the reflection scheme) which is an analogue of the reflection principle of Zermelo-Fraenkel set theory. Here ${\mathcal{L}}$ is a language with a distinguished linear order <, and REF ${(\mathcal {L})}$ consists of formulas of the form $$\exists x \forall y_{1} < x \ldots \forall y_{n} < x \varphi (y_{1},\ldots ,y_{n})\leftrightarrow \varphi^{ < x}(y_1, \ldots ,y_n),$$ where φ is an ${\mathcal{L}}$ -formula, φ
Keywords Mathematics   Algebra   Mathematics, general   Mathematical Logic and Foundations
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DOI 10.1007/s00153-008-0089-z
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References found in this work BETA

Subsystems of Second-Order Arithmetic.Stephen G. Simpson - 2004 - Studia Logica 77 (1):129-129.
The Fine Structure of the Constructible Hierarchy.R. Björn Jensen - 1972 - Annals of Pure and Applied Logic 4 (3):229.
Powers of Regular Cardinals.William B. Easton - 1970 - Annals of Pure and Applied Logic 1 (2):139.
Blunt and Topless End Extensions of Models of Set Theory.Matt Kaufmann - 1983 - Journal of Symbolic Logic 48 (4):1053-1073.

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