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Related papers: Characterizations of monadic NIP

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We prove that for every simple theory $T$ (or even simple thick compact abstract theory) there is a (unique) compact abstract theory $T^\fP$ whose saturated models are the lovely pairs of $T$. Independence-theoretic results that were proved…

Logic · Mathematics 2009-02-05 Itaï Ben Yaacov

A first-order theory $T$ is a model-complete core theory if every first-order formula is equivalent modulo $T$ to an existential positive formula; the core companion of a theory $T$ is a model-complete core theory $S$ such that every model…

Logic · Mathematics 2025-12-25 Manuel Bodirsky , Bertalan Bodor , Paolo Marimon

We consider the following property of a first order theory T with a distinguished unary predicate P: every model of the theory of P occurs as the P-part of some model of T. We call this property the Gaifman property. Gaifman conjectured…

Logic · Mathematics 2025-07-18 Saharon Shelah , Alexander Usvyatsov

Monadic decomposability is a notion of variable independence, which asks whether a given formula in a first-order theory is expressible as a Boolean combination of monadic predicates in the theory. Recently, Veanes et al. showed the…

Logic in Computer Science · Computer Science 2020-04-28 Matthew Hague , Anthony Widjaja Lin , Philipp Rümmer , Zhilin Wu

Monadically stable and monadically NIP classes of structures were initially studied in the context of model theory and defined in logical terms. They have recently attracted attention in the area of structural graph theory, as they…

Logic in Computer Science · Computer Science 2023-11-28 Jan Dreier , Nikolas Mählmann , Sebastian Siebertz , Szymon Toruńczyk

The class of problems complete for NP via first-order reductions is known to be characterized by existential second-order sentences of a fixed form. All such sentences are built around the so-called generalized IS-form of the sentence that…

Computational Complexity · Computer Science 2007-06-26 Nerio Borges , Blai Bonet

We prove completeness, interpolation and omitting types for certain predicate topological logics that properly extend the first order case. We aslo count the non isomorphic topological models of a countable theory

Logic · Mathematics 2013-04-08 Tarek Sayed Ahmed

A dependent theory is a (first order complete theory) T which does not have the independence property. A main result here is: if we expand a model of T by the traces on it of sets definable in a bigger model then we preserve its being…

Logic · Mathematics 2013-02-20 Saharon Shelah

We introduce the notion of hereditary G-compactness (with respect to interpretation). 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.…

Logic · Mathematics 2022-03-11 Tomasz Rzepecki

Krebs et al. (2007) gave a characterization of the complexity class TC0 as the class of languages recognized by a certain class of typed monoids. The notion of typed monoid was introduced to extend methods of algebraic automata theory to…

Logic in Computer Science · Computer Science 2025-08-18 Anuj Dawar , Aidan T. Evans

We investigate the extent of second order characterizable structures by extending Shelah's Main Gap dichotomy to second order logic. For this end we consider a countable complete first order theory T. We show that all sufficiently large…

Logic · Mathematics 2012-08-28 Tapani Hyttinen , Kaisa Kangas , Jouko Väänänen

We introduce the notion of strong $p$-semi-regularity and show that if $p$ is a regular type which is not locally modular then any $p$-semi-regular type is strongly $p$-semi-regular. Moreover, for any such $p$-semi-regular type, "domination…

Logic · Mathematics 2024-04-16 Elisabeth Bouscaren , Bradd Hart , Ehud Hrushovski , Michael C. Laskowski

We introduce the notion of first order amenability, as a property of a first order theory $T$: every complete type over $\emptyset$, in possibly infinitely many variables, extends to an automorphism-invariant global Keisler measure in the…

Logic · Mathematics 2025-11-18 Ehud Hrushovski , Krzysztof Krupiński , Anand Pillay

Model theoretic results such as Characterization and Definability give important information about different logics. It is well known that the proofs of those results for several modal logics have, somehow, the same 'taste'. A general proof…

Logic in Computer Science · Computer Science 2010-11-23 Facundo Carreiro

We study the properties of algebraic independence and pointwise algebraic independence in a class of continuous theories, the randomizations $T^R$ of complete first order theories $T$. If algebraic and definable closure coincide in $T$,…

Logic · Mathematics 2017-04-03 Uri Andrews , Isaac Goldbring , H. Jerome Keisler

Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions…

cmp-lg · Computer Science 2008-02-03 Rolf Backofen , Gert Smolka

The randomization of a complete first order theory T is the complete continuous theory T^R with two sorts, a sort for random elements of models of T, and a sort for events in an underlying probability space. We give necessary and sufficient…

Logic · Mathematics 2013-05-01 Uri Andrews , Isaac Goldbring , H. Jerome Keisler

We define the continuous modeling property for first-order structures and show that a first-order structure has the continuous modelling property if and only if its age has the embedding Ramsey property. We use generalized indiscernible…

Logic · Mathematics 2024-05-31 Adrián Portillo Fernández

In this short note we show that if we add predicate for a dense complete indiscernible sequence in a dependent theory then the result is still dependent. This answers a question of Baldwin and Benedikt and implies that every unstable…

Logic · Mathematics 2009-06-16 Artem Chernikov , Pierre Simon

In this note we study sets of NIP formulas in some theories of fields and valued fields, with a special focus on the sets of quantifier-free and existential formulas. First, we give a new proof of the fact that Separably Closed Valued…

Logic · Mathematics 2026-02-04 Paulo Andrés Soto Moreno