arXiv subjects

Joni Puljujärvi

Publications and source records attributed to Joni Puljujärvi.

6 recordsLinked to original sources

arXiv2026

A New Ehrenfeucht-Fraïssé Game for Dependence Logic

We define a new Ehrenfeucht-Fraïssé game for dependence logic. The previously known rendition of such a game was based on moves that are teams. Since teams can be massive, making team moves may be quite complicated. To remedy this, our new Ehrenfeucht-Fraïssé game for dependence logic has only moves that consist of single elements, as in the classical Ehrenfeucht-Fraïssé game of first order logic. A new feature of the game is that a player can declare that their move is made on the basis of certain previous moves only and thereby in a sense independent of other moves. We show that our game characterizes elementary equivalence in dependence logic.

math.LO↗

arXiv2026

On the Model Theory of Second-Order Objects

Motivated by team semantics and existential second-order logic, we develop a model-theoretic framework for studying second-order objects such as sets and relations. We introduce a notion of abstract elementary team categories that generalizes the standard notion of abstract elementary class, and show that it is an example of an accessible category. We apply our framework to show that the logic $\mathsf{FOT}$ introduced by Kontinen and Yang satisfies a version of Lindström's Theorem. Finally, we consider the problem of transferring categoricity between different cardinalities for complete theories in existential second-order logic (or independence logic) and prove both a downwards and an upwards categoricity transfer result.

math.LO↗

arXiv2025

Team Semantics and Independence Notions in Quantum Physics

We study dependence and independence concepts found in quantum physics, especially those related to hidden variables and non-locality, through the lens of team semantics and probabilistic team semantics, adapting a relational framework introduced by the first author in a prior paper. This leads to new developments also in independence logic and probabilistic independence logic.

math.LO↗

arXiv2024

Ehrenfeucht-Fraïssé Games for Continuous First-Order Logic

We define a version of the Ehrenfeucht-Fraïssé game in the setting of metric model theory and continuous first-order logic and show that the second player having a winning strategy in a game of length $n$ exactly corresponds to being elementarily equivalent up to quantifier rank $n$. We then demonstrate the usefulness of the game with some examples. Finally, we discus connections between the game of length $ω$ and infinitary logic.

math.LO↗

arXiv2022

Compactness in Team Semantics

We provide two proofs of the compactness theorem for extensions of first-order logic based on team semantics. First, we build upon Lück's ultraproduct construction for team semantics and prove a suitable version of Łoś' Theorem. Second, we show that by working with suitably saturated models, we can generalize the proof of Kontinen and Yang to sets of formulas with arbitrarily many variables.

math.LO↗

arXiv2021

Games and Scott sentences for positive distances between metric structures

We develop various Ehrenfeucht-Fra\"ıssé games for distances between metric structures. We study two forms of distances: pseudometrics stemming from mapping spaces onto each other with some form of approximate isomorphism, and metrics stemming from measuring the distances between two spaces isometrically embedded into a third space. Using an infinitary version of Henson's positive bounded logic with approximations, we form Scott sentences capturing fixed distances to a given space. The Scott sentences of separable spaces are in $\mathcal{L}_{ω_1ω}$ for 0-distances and in $\mathcal{L}_{ω_2ω}$ for positive distances.

math.LO↗