scholarly journals ON DEFINABLE SKOLEM FUNCTIONS IN WEAKLY O-MINIMAL NONVALUATIONAL STRUCTURES

2017 ◽  
Vol 82 (4) ◽  
pp. 1482-1495 ◽  
Author(s):  
PANTELIS E. ELEFTHERIOU ◽  
ASSAF HASSON ◽  
GIL KEREN
Keyword(s):  

AbstractWe prove that all known examples of weakly o-minimal nonvaluational structures have no definable Skolem functions. We show, however, that such structures eliminate imaginaries up to definable families of cuts. Along the way we give some new examples of weakly o-minimal nonvaluational structures.

1972 ◽  
Vol 37 (1) ◽  
pp. 114-132 ◽  
Author(s):  
Erik Ellentuck

In this paper we show (cf. Theorem 22) that in a language L* with equality, whose relation symbols denote arbitrary relations over ω* (=rational integers) and whose function symbols denote (= ∃∀ definable in the arithmetic hierarchy) functions over ω*, (i) a positive sentence is true in Λ* (= isolic integers) iff some Horn reduct is true in ω* with Skolem functions. We also show (cf Theorem 20) that (ii) a universally quantified sentence is true in Λ* iff some Horn reduct is true in Λ*.The latter result is nontrivial because our relations are arbitrary and our functions are In order to obtain (i) it was necessary to generalize the frame extensions of [7]. This is done in §2. Our extension procedure agrees with that of [7] for recursive relations (cf. Theorem 12), and is certainly more general for − relations. What happens in the case is still open. In §3 we develop the basic properties of our extension so that in §4 we can prove a metatheorem (cf. Theorems 8 and 10) about Λ (=isols), in a language L with equality whose relation symbols denote arbitrary relations over ω (=nonnegative integers) and whose function symbols denote almost R↑ combinatorial functions. In Theorem 11 this is generalized to infinitary universal sentences. In §5 generic isols are introduced. These are used (cf. Theorems 16–19) to generalize and simplify the “fundamental lemma” of [8]. The basic induction is patterned after Lemma 4.1 of [8], but is stronger in that any sufficiently generic assignment attainable from a frame yields Skolem functions. Finally in §6 these results are applied to Λ*, yielding the titled result (i) of our paper. Immediately following Theorem 15 there is a discussion which attempts to justify the way we extend relations to Λ.


1998 ◽  
Vol 63 (1) ◽  
pp. 103-127 ◽  
Author(s):  
Shmuel Lifsches ◽  
Saharon Shelah

AbstractThe monadic second-order theory of trees allows quantification over elements and over arbitrary subsets. We classify the class of trees with respect to the question: does a tree T have definable Skolem functions (by a monadic formula with parameters)? This continues [6] where the question was asked only with respect to choice functions. A natural subclass is defined and proved to be the class of trees with definable Skolem functions. Along the way we investigate the spectrum of definable well orderings of well ordered chains.


2018 ◽  
Vol 41 ◽  
Author(s):  
Maria Babińska ◽  
Michal Bilewicz

AbstractThe problem of extended fusion and identification can be approached from a diachronic perspective. Based on our own research, as well as findings from the fields of social, political, and clinical psychology, we argue that the way contemporary emotional events shape local fusion is similar to the way in which historical experiences shape extended fusion. We propose a reciprocal process in which historical events shape contemporary identities, whereas contemporary identities shape interpretations of past traumas.


2020 ◽  
Vol 43 ◽  
Author(s):  
Aba Szollosi ◽  
Ben R. Newell

Abstract The purpose of human cognition depends on the problem people try to solve. Defining the purpose is difficult, because people seem capable of representing problems in an infinite number of ways. The way in which the function of cognition develops needs to be central to our theories.


1976 ◽  
Vol 32 ◽  
pp. 233-254
Author(s):  
H. M. Maitzen

Ap stars are peculiar in many aspects. During this century astronomers have been trying to collect data about these and have found a confusing variety of peculiar behaviour even from star to star that Struve stated in 1942 that at least we know that these phenomena are not supernatural. A real push to start deeper theoretical work on Ap stars was given by an additional observational evidence, namely the discovery of magnetic fields on these stars by Babcock (1947). This originated the concept that magnetic fields are the cause for spectroscopic and photometric peculiarities. Great leaps for the astronomical mankind were the Oblique Rotator model by Stibbs (1950) and Deutsch (1954), which by the way provided mathematical tools for the later handling pulsar geometries, anti the discovery of phase coincidence of the extrema of magnetic field, spectrum and photometric variations (e.g. Jarzebowski, 1960).


Author(s):  
W.M. Stobbs

I do not have access to the abstracts of the first meeting of EMSA but at this, the 50th Anniversary meeting of the Electron Microscopy Society of America, I have an excuse to consider the historical origins of the approaches we take to the use of electron microscopy for the characterisation of materials. I have myself been actively involved in the use of TEM for the characterisation of heterogeneities for little more than half of that period. My own view is that it was between the 3rd International Meeting at London, and the 1956 Stockholm meeting, the first of the European series , that the foundations of the approaches we now take to the characterisation of a material using the TEM were laid down. (This was 10 years before I took dynamical theory to be etched in stone.) It was at the 1956 meeting that Menter showed lattice resolution images of sodium faujasite and Hirsch, Home and Whelan showed images of dislocations in the XlVth session on “metallography and other industrial applications”. I have always incidentally been delighted by the way the latter authors misinterpreted astonishingly clear thickness fringes in a beaten (”) foil of Al as being contrast due to “large strains”, an error which they corrected with admirable rapidity as the theory developed. At the London meeting the research described covered a broad range of approaches, including many that are only now being rediscovered as worth further effort: however such is the power of “the image” to persuade that the above two papers set trends which influence, perhaps too strongly, the approaches we take now. Menter was clear that the way the planes in his image tended to be curved was associated with the imaging conditions rather than with lattice strains, and yet it now seems to be common practice to assume that the dots in an “atomic resolution image” can faithfully represent the variations in atomic spacing at a localised defect. Even when the more reasonable approach is taken of matching the image details with a computed simulation for an assumed model, the non-uniqueness of the interpreted fit seems to be rather rarely appreciated. Hirsch et al., on the other hand, made a point of using their images to get numerical data on characteristics of the specimen they examined, such as its dislocation density, which would not be expected to be influenced by uncertainties in the contrast. Nonetheless the trends were set with microscope manufacturers producing higher and higher resolution microscopes, while the blind faith of the users in the image produced as being a near directly interpretable representation of reality seems to have increased rather than been generally questioned. But if we want to test structural models we need numbers and it is the analogue to digital conversion of the information in the image which is required.


1979 ◽  
Vol 44 (1) ◽  
pp. 3-30 ◽  
Author(s):  
Carol A. Pruning

A rationale for the application of a stage process model for the language-disordered child is presented. The major behaviors of the communicative system (pragmatic-semantic-syntactic-phonological) are summarized and organized in stages from pre-linguistic to the adult level. The article provides clinicians with guidelines, based on complexity, for the content and sequencing of communicative behaviors to be used in planning remedial programs.


ASHA Leader ◽  
2013 ◽  
Vol 18 (2) ◽  
pp. 5-7 ◽  
Author(s):  
Patty Prelock

Children with disabilities benefit most when professionals let families lead the way.


Sign in / Sign up

Export Citation Format

Share Document