2021arXiv (Cornell University)Open access

Reconstruction of non-$\aleph_0$-categorical theories

Itaï Ben Yaacov

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Abstract

We generalise the correspondence between $\aleph 0$-categorical theories and their automorphism groups to arbitrary complete theories in classical logic, and to some theories (including, in particular, all $\aleph 0$-categorical ones) in continuous logic.

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We generalise the correspondence between $\aleph 0$-categorical theories and their automorphism groups to arbitrary complete theories in classical logic, and to some theories (including, in particular, all $\aleph 0$-categorical ones) in continuous logic.

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Available abstract

We generalise the correspondence between $\aleph 0$-categorical theories and their automorphism groups to arbitrary complete theories in classical logic, and to some theories (including, in particular, all $\aleph 0$-categorical ones) in continuous logic.

Key concepts: Aleph, Categorical variable, Mathematics, Automorphism, Algebra over a field, Pure mathematics, Philosophy, Statistics

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