Related papers: EF equivalent not isomorphic models
Ehrenfeucht-Fra\"iss\'e (EF) games are a basic tool in finite model theory for proving definability lower bounds, with many applications in complexity theory and related areas. They have been applied to study various logics, giving insights…
We study the classification of omega_1-separable groups using Ehrenfeucht-Fraisse games and prove a strong classification result assuming PFA, and a strong non-structure theorem assuming diamond.
A modeloid, a certain set of partial bijections, emerges from the idea to abstract from a structure to the set of its partial automorphisms. It comes with an operation, called the derivative, which is inspired by Ehrenfeucht-Fra\"iss\'e…
Multi-structural (MS) games are combinatorial games that capture the number of quantifiers of first-order sentences. On the face of their definition, MS games differ from Ehrenfeucht-Fraisse (EF) games in two ways: first, MS games are…
Truth, consistency and elementary equivalence can all be characterised in terms of games, namely the so-called evaluation game, the model-existence game, and the Ehrenfeucht-Fraisse game. We point out the great affinity of these games to…
We study multi-structural games, played on two sets $\mathcal{A}$ and $\mathcal{B}$ of structures. These games generalize Ehrenfeucht-Fra\"{i}ss\'{e} games. Whereas Ehrenfeucht-Fra\"{i}ss\'{e} games capture the quantifier rank of a…
Let $f: M \to M$ be a partially hyperbolic diffeomorphism with conformality on unstable manifolds. Consider a set of points with nondense forward orbit: $E(f, y) := \{ z\in M: y\notin \overline{\{f^k(z), k \in \mathbb{N}\}}\}$ for some $y…
Despite considerable research on document spanners, little is known about the expressive power of generalized core spanners. In this paper, we use Ehrenfeucht-Fra\"iss\'e games to obtain general inexpressibility lemmas for the logic FC (a…
The authors show, by means of a finitary version square^{fin}_{lambda,D} of the combinatorial principle square^{b^*}_{lambda}, the consistency of the failure, relative to the consistency of supercompact cardinals, of the following: for all…
This paper has two parts. The first is concerned with a variant of a family of games introduced by Holy and Schlicht, that we call \emph{Welch games}. Player II having a winning strategy in the Welch game of length $\omega$ on $\kappa$ is…
We construct a pair (E ,F), where E is a holomorphic vector bundle over a compact Riemann surface and F a holomorphic subbundle of E, such that both F and E/F admit holomorphic connections, but E does not.
While many types of non-measurable sets are never $(\alpha, \beta)$-winning in the sense of Schmidt's game, we show that this is not the case for certain Vitali sets. Our main theorems show that for certain values of $\alpha, \beta$ one can…
Recently, Boutonnet, Chifan, and Ioana proved that McDuff's examples of continuum many pairwise non-isomorphic separable II$_1$ factors are in fact pairwise non-elementarily equivalent. Their proof proceeded by showing that any ultrapowers…
We introduce differential games for FO logic of graphs, a variant of Ehrenfeucht-Fra\"{i}ss\'e games in which the game is played on only one graph and the moves of both players restricted. We prove that, in a certain sense, these games are…
Fragments of first-order logic over words can often be characterized in terms of finite monoids, and identities of omega-terms are an effective mechanism for specifying classes of monoids. Huschenbett and the first author have shown how to…
Recently, Boutonnet, Chifan, and Ioana proved that McDuff's family of continuum many pairwise nonisomorphic separable II$_1$ factors are in fact pairwise non-elementarily equivalent by proving that any ultrapowers of two distinct members of…
We extend the inflationary fixed-point logic, IFP, with a new kind of second-order quantifiers which have (poly-)logarithmic bounds. We prove that on ordered structures the new logic $\exists^{\log^{\omega}}\text{IFP}$ captures the limited…
We give an example of irrational vector $\pmb{\theta} \in \mathbb{R}^2$ such that the set $Bad_{\pmb{\theta}} := \{(\eta_1,\eta_2): \inf_{x\in\mathbb{N}} x^{\frac{1}{2}} \max_{i=1,2} \|x \theta_i-\eta_i\|>0\}$ is not absolutely winning with…
We study the problem of computing an Extensive-Form Perfect Equilibrium (EFPE) in 2-player games. This equilibrium concept refines the Nash equilibrium requiring resilience w.r.t. a specific vanishing perturbation (representing mistakes of…
We construct (\alpha ,\beta) and \alpha -winning sets in the sense of Schmidt's game, played on the support of certain measures (very friendly and awfully friendly measures) and show how to derive the Hausdorff dimension for some. In…