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      Combining Finite Combination Properties: Finite Models and Busy Beavers

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          Abstract

          This work is a part of an ongoing effort to understand the relationships between properties used in theory combination. We here focus on including two properties that are related to shiny theories: the finite model property and stable finiteness. For any combination of properties, we consider the question of whether there exists a theory that exhibits it. When there is, we provide an example with the simplest possible signature. One particular class of interest includes theories with the finite model property that are not finitely witnessable. To construct such theories, we utilize the Busy Beaver function.

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          Author and article information

          Journal
          15 July 2023
          Article
          2307.07885
          34674be3-1b3e-4fbd-a2d0-12a169835350

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          cs.LO

          Theoretical computer science
          Theoretical computer science

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