This paper continues [DjSh692]. We present a rank function for NSOP1 theories and give an example of a theory which is NSOP1 but not simple. We also investigate the connection between maximality in the ordering ⊳ among complete first order theories and the (N)SOP2 property. We complete the proof started in [DjSh692] of the fact that ⊳-maximality implies SOP2 and get weaker results in the other ...

Within a nonzero, real Banach space we study the problem of characterising a maximal extension of a monotone operator in terms of minimality properties of representative functions that are bounded by the Penot and Fitzpatrick functions. We single out a property of this space of representative functions that enable a very compact treatment of maximality and pre-maximality issues. This Paper is D...

Recent research suggests that outcome additivity pretraining modulates blocking in human causal learning. However, the existing evidence confounds outcome additivity and outcome maximality. Here the authors present evidence for the influence of presenting information about outcome maximality (Experiment 1) and outcome additivity (Experiment 2) on subsequent forward blocking. The results of Expe...

This paper investigates a connection between the semantic notion provided by the ordering C∗ among theories in model theory and the syntactic (N)SOPn hierarchy of Shelah. It introduces two properties which are natural extensions of this hierarchy, called SOP2 and SOP1. It is shown here that SOP3 implies SOP2 implies SOP1. In [Sh 500] it was shown that SOP3 implies C ∗-maximality and we prove he...

The paper explores the polyfunctional word 都 to TO in early Southern Min texts dating back to the sixteenth century or even earlier. Unlike 都 dou in Mandarin, which mainly functions as a maximality operator, 都 to in Southern Min is chiefly used as a modal particle expressing a concessive meaning or meaning of unexpectedness as a type of conventional implicature rather than pragmatic inference. ...

We consider recognizability for Infinite Time Blum-Shub-Smale machines, a model of infinitary computability introduced by Koepke and Seyfferth. In particular, we show that the lost melody theorem (originally proved ITTMs Hamkins Lewis), i.e. existence non-computable, but recognizable real numbers, holds ITBMs, ITBM-recognizable numbers are hyperarithmetic both ITBM-unrecognizable appear at ever...

The notion of a strictly maximal point is a concept of proper maximality that plays an important role in the study of the stability of vector optimization problems. The aim of this paper is to study some properties of this notion with particular attention to geometrical aspects. More precisely, we individuate some relationships between strict maximality and the properties of the bases of the or...