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  1. Hereditary G-compactness.Tomasz Rzepecki - 2021 - Archive for Mathematical Logic 60 (7):837-856.
    We introduce the notion of hereditary G-compactness. We provide a sufficient condition for a poset to not be hereditarily G-compact, which we use to show that any linear order is not hereditarily G-compact. Assuming that a long-standing conjecture about unstable NIP theories holds, this implies that an NIP theory is hereditarily G-compact if and only if it is stable -categorical theories). We show that if G is definable over A in a hereditarily G-compact theory, then \. We also include a (...)
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  • On Vapnik‐Chervonenkis density over indiscernible sequences.Vincent Guingona & Cameron Donnay Hill - 2014 - Mathematical Logic Quarterly 60 (1-2):59-65.
    In this paper, we study Vapnik‐Chervonenkis density (VC‐density) over indiscernible sequences (denoted VCind‐density). We answer an open question in [1], showing that VCind‐density is always integer valued. We also show that VCind‐density and dp‐rank coincide in the natural way.
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  • On VC-minimal fields and dp-smallness.Vincent Guingona - 2014 - Archive for Mathematical Logic 53 (5-6):503-517.
    In this paper, we show that VC-minimal ordered fields are real closed. We introduce a notion, strictly between convexly orderable and dp-minimal, that we call dp-small, and show that this is enough to characterize many algebraic theories. For example, dp-small ordered groups are abelian divisible and dp-small ordered fields are real closed.
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  • On VC-Density in VC-Minimal Theories.Vincent Guingona - 2022 - Notre Dame Journal of Formal Logic 63 (3):395-413.
    We show that any formula with two free variables in a Vapnik–Chervonenkis (VC) minimal theory has VC-codensity at most 2. Modifying the argument slightly, we give a new proof of the fact that, in a VC-minimal theory where acleq= dcleq, the VC-codensity of a formula is at most the number of free variables (from the work of Aschenbrenner et al., the author, and Laskowski).
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  • Semi-Equational Theories.Artem Chernikov & Alex Mennen - forthcoming - Journal of Symbolic Logic:1-32.
    We introduce and study (weakly) semi-equational theories, generalizing equationality in stable theories (in the sense of Srour) to the NIP context. In particular, we establish a connection to distality via one-sided strong honest definitions; demonstrate that certain trees are semi-equational, while algebraically closed valued fields are not weakly semi-equational; and obtain a general criterion for weak semi-equationality of an expansion of a distal structure by a new predicate.
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