119 Citations
CODING IN GRAPHS AND LINEAR ORDERINGS
- Mathematics, Computer ScienceThe Journal of Symbolic Logic
- 2020
It is shown that there is no fixed tuple of formulas that, for all G, interpret the input graph G in the output linear ordering $L(G)$ .
The Craig Interpolation Theorem in abstract model theory
- Philosophy, MathematicsSynthese
- 2008
It is argued in this paper that the interpolation property is an important litmus test in abstract model theory for identifying “natural,” robust extensions of first order logic.
Interpolation Theorem and Characterization Theorem
- Mathematics
- 1972
Introduction In this paper, we shall show some examples of the applications of "normal derivation theorem" in Motohashi [27] to a new kind of problems named "inter polation problem and…
Generic length functions on countable groups
- Mathematics
- 2022
Let L p G q denote the space of integer-valued length functions on a countable group G endowed with the topology of pointwise convergence. Assuming that G does not satisfy any non-trivial mixed…
Characterizing the existence of a Borel complete expansion
- Mathematics
- 2021
We develop general machinery to cast the class of potential canonical Scott sentences of an infinitary sentence Φ as a class of structures in a related language. From this, we show that Φ has a Borel…
LOGICALITY AND MODEL CLASSES
- PhilosophyThe Bulletin of Symbolic Logic
- 2021
Abstract We ask, when is a property of a model a logical property? According to the so-called Tarski–Sher criterion this is the case when the property is preserved by isomorphisms. We relate this to…
AN INTRODUCTION TO THE SCOTT COMPLEXITY OF COUNTABLE STRUCTURES AND A SURVEY OF RECENT RESULTS
- PhilosophyThe Bulletin of Symbolic Logic
- 2021
Abstract Every countable structure has a sentence of the infinitary logic
$\mathcal {L}_{\omega _1 \omega }$
which characterizes that structure up to isomorphism among countable structures. Such a…
A topological zero-one law and elementary equivalence of finitely generated groups
- MathematicsAnn. Pure Appl. Log.
- 2021
SCOTT COMPLEXITY OF COUNTABLE STRUCTURES
- MathematicsThe Journal of Symbolic Logic
- 2021
Abstract We define the Scott complexity of a countable structure to be the least complexity of a Scott sentence for that structure. This is a finer notion of complexity than Scott rank: it…
Scott sentences for equivalence structures
- MathematicsArch. Math. Log.
- 2020
An example of a particular equivalence structure for which the index set is m -complete but for which there is no computable Π 3 pseudo-Scott sentence is given, that is, a sentence that acts as a Scott sentence if the authors only consider computable structures.