Generalizing classical and effective model theory in theories of operations and classes
type: Item
instance of: scholarly article
title: Generalizing classical and effective model theory in theories of operations and classes
zbMATH Open document ID: 0733.03030
DOI: 10.1016/0168-0072(91)90032-H
author: Paolo Mancosu
published in: Annals of Pure and Applied Logic
publication date: 1991-01-01T00:00:00Z
review text: The author proposes a family of theories of operations and classes with an aim of developing abstract versions of model-theoretic results. The theories in question are two-sorted, with one kind of variable for individuals and the other for classes. All the theories used assume a common group of axioms. The author works mainly with three theories, \(FMT_ 0\), FMT, \(FMT_{\Omega}\). The aim of the author's work is to give an abstract development of model theory in these theories and in a way to look as much as possible like classical mathematics. \(FMT_ 0\) generalizes portions of countable and recursive model theory; FMT generalizes portions of countable and hyperarithmetical model theory and \(FMT_{\Omega}\) provides a generalization of the classical L(Q)- completeness theorem and of an admissible version of L(Q)-completeness due to Bruce and Keisler. The paper continues the program originated by Feferman.
Mathematics Subject Classification ID: 03C95
Mathematics Subject Classification ID: 03C57
Mathematics Subject Classification ID: 03C70
Mathematics Subject Classification ID: 03C15
zbMATH DE Number: 4212025
zbMATH Keywords: countable model theory
zbMATH Keywords: theories of operations and classes
zbMATH Keywords: recursive model theory
zbMATH Keywords: hyperarithmetical model theory
zbMATH Keywords: L(Q)-completeness
MaRDI profile type: Publication
cites work: Q4075450
cites work: An introduction to recursively saturated and resplendent models
cites work: LA(Ⅎ)
cites work: Iterated inductive definitions and subsystems of analysis: recent proof-theoretical studies
cites work: Model theory
cites work: Q5620597
cites work: Recursive categoricity and recursive stability
cites work: Model theory on admissible sets
cites work: Q3958432
cites work: Q4128540
cites work: Generalized recursion theory II. Proceedings of the 1977 Oslo Symposium
cites work: Q3882452
cites work: Q3880813
cites work: Q3663255
cites work: Intensionality in mathematics
cites work: Q4698612
cites work: Countable algebra and set existence axioms
cites work: Stability theory and set existence axioms
cites work: Set existence axioms for general (not necessarily countable) stability theory
cites work: Recursively presentable prime models
cites work: Logic with the quantifier “there exist uncountably many”
cites work: Model theory for infinitary logic. Logic with countable conjunctions and finite quantifiers
cites work: Foundations of recursive model theory
cites work: Q4124795
cites work: Decidable models
cites work: Q5600870
cites work: Q5573961
cites work: Toward model theory through recursive saturation
cites work: Q3699664
cites work: Q3395521
cites work: Undecidable theories
full work available at URL: 0168-0072(91)90032-h
OpenAlex ID: W2033882622
description: scientific article; zbMATH DE number 4212025