In this paper, we investigate definable models of Peano Arithmetic PA in a model of PA. For any definable model N without parameters in a model M, we show that N is isomorphic to M if M is elementary extension of the standard model and N is elementarily equivalent to M. On the other hand, we show that there is a model M and a definable model N with parameters in M such that N is elementarily equivalent to M but (...) N is not isomorphic to M. We also show that there is a model M and a definable model N with parameters in M such that N is elementarily equivalent to M, and N is isomorphic to M, but N is not definably isomorphic to M. And also, we give a generalization of Tennenbaum's theorem. At the end, we give a new method to construct a definable model by a refinement of Kotlarski's method. (shrink)

Facial expressions influence our experience and perception of emotions—they not only tell other people what we are feeling but also might tell us what to feel via sensory feedback. We conducted three experiments to investigate the interaction between facial feedback phenomena and different environmental stimuli, by asking participants to remember emotional autobiographical memories. Moreover, we examined how people with schizotypal traits would be affected by their experience of emotional facial simulations. We found that using a directed approach (gripping a pencil (...) with teeth/lips) while remembering a specific autobiographical memory could successfully evoke participants’ positive (e.g. happy and excited)/negative (e.g. angry and sad) emotions (i.e. Experiment 1). When using indirective environmental stimuli (e.g. teardrop glasses), the results of our experiments (i.e. Experiments 2 and 3) investigating facial feedback and the effect of teardrop glasses showed that participants who scored low in schizotypy reported little effect from wearing teardrop glasses, while those with high schizotypy reported a much greater effect in both between- and within-subject conditions. The results are discussed from the perspective of sense of ownership, which people with schizophrenia are believed to have deficits in. (shrink)