IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i3p461-d739205.html
   My bibliography  Save this article

Interpolation and Uniform Interpolation in Quantifier-Free Fragments of Combined First-Order Theories

Author

Listed:
  • Silvio Ghilardi

    (Department of Mathematics, Universitá degli Studi di Milano, 20133 Milan, Italy)

  • Alessandro Gianola

    (Faculty of Computer Science, Free University of Bozen-Bolzano, 39100 Bolzano, Italy)

Abstract

In this survey, we report our recent work concerning combination results for interpolation and uniform interpolation in the context of quantifier-free fragments of first-order theories. We stress model-theoretic and algebraic aspects connecting this topic with amalgamation, strong amalgamation, and model-completeness. We give sufficient (and, in relevant situations, also necessary) conditions for the transfer of the quantifier-free interpolation property to combined first-order theories; we also investigate the non-disjoint signature case under the assumption that the shared theory is universal Horn. For convex, strong-amalgamating, stably infinite theories over disjoint signatures, we also provide a modular transfer result for the existence of uniform interpolants. Model completions play a key role in the whole paper: They enter into transfer results in the non-disjoint signature case and also represent a semantic counterpart of uniform interpolants.

Suggested Citation

  • Silvio Ghilardi & Alessandro Gianola, 2022. "Interpolation and Uniform Interpolation in Quantifier-Free Fragments of Combined First-Order Theories," Mathematics, MDPI, vol. 10(3), pages 1-22, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:461-:d:739205
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/3/461/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/3/461/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:461-:d:739205. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.