Computable model theory
نویسندگان
چکیده
منابع مشابه
Infinite Time Computable Model Theory
We introduce infinite time computable model theory, the computable model theory arising with infinite time Turing machines, which provide infinitary notions of computability for structures built on the reals R. Much of the finite time theory generalizes to the infinite time context, but several fundamental questions, including the infinite time computable analogue of the Completeness Theorem, t...
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We give effectiveness conditions on a strongly minimal theory T guaranteeing that all models have computable copies. In particular, we show that if T is strongly minimal and for n ě 1, T X Dn`2 is ∆n, uniformly in n, then every model has a computable copy. Relativizing, we answer a long-standing question in computable model theory, showing that if a strongly minimal theory has a computable mode...
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An important theme in computable model theory is the study of computable models of complete first-order theories. More precisely, given a complete firstorder theory T , one would like to know which models of T have computable copies and which do not. A special case of interest is when T is an א1-categorical theory. In this paper we are interested in computable models of א1-categorical theories....
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This survey paper examines the effective model theory obtained with the BSS model of real number computation. It treats the following topics: computable ordinals, satisfaction of computable infinitary formulas, forcing as a construction technique, effective categoricity, effective topology, and relations with other models for the effective theory of uncountable structures.
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The theory of computable models is an intensively developing area of mathematics that studies the interactions between the theory of models and computability theory. Analyzing the relationships between computable presentations of models, model-theoretic definability and the computable complexity of relations is one of the central problems in this area. A fundamental notion in the study of these...
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تاریخ انتشار 2014