Publication details
Positively closed Sh(B)-valued models
| Authors | |
|---|---|
| Year of publication | 2026 |
| Type | Article in Periodical |
| Magazine / Source | ANNALS OF PURE AND APPLIED LOGIC |
| MU Faculty or unit | |
| Citation | |
| web | https://www.sciencedirect.com/science/article/pii/S0168007226000096 |
| Doi | https://doi.org/10.1016/j.apal.2026.103726 |
| Keywords | Grothendieck topos; Internal model; Positively closed model |
| Attached files | |
| Description | We study positively closed and strongly positively closed topos-valued models of coherent theories. Positively closed is a global notion (it is defined in terms of all possible outgoing homomorphisms), while strongly positively closed is a local notion (it only concerns the definable sets inside the model). For Set-valued models of coherent theories they coincide. We prove that if E = Sh(B,tau coh) for a complete Boolean algebra, then positively closed but not strongly positively closed E-valued models of coherent theories exist, yet, there is an alternative local property which characterizes positively closed E-valued models. A large part of our discussion is given in the context of infinite quantifier geometric logic, dealing with the fragment Lg kappa kappa where kappa is weakly compact. (c) 2026 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). |
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