We characterize the ω-stable theories all of whose countable models admit decidable presentations. In particular, we show that for a countable ω-stable T , every countable model of T admits a decidable presentation if and only if all n-types in T are recursive and T has only countably many countable models. We further characterize the decidable models of ω-stable theories with countably many co...

1 Probability Theory over Countable Spaces Definition 1 (Countable Probability Space). A Countable Probability Space is composed of the tuple (Ω,Pr). • Countable Sample Space Ω The sample space is a set of outcomes for a particular experiment. “Countable” means that either the size of Ω is finite or there is a one-to-one and onto correspondence between the the elements of Ω and the set of Natur...

In recent years, much work in descriptive set theory has been focused on the Borel complexity of naturally occurring classification problems, in particular, the study of countable Borel equivalence relations and their structure under the quasi-order of Borel reducibility. Following the approach of Louveau and Rosendal in [8] for the study of analytic equivalence relations, we study countable Bo...

In this paper, countable compactness and the Lindel¨of propertyare defined for L-fuzzy sets, where L is a complete de Morgan algebra. Theydon’t rely on the structure of the basis lattice L and no distributivity is requiredin L. A fuzzy compact L-set is countably compact and has the Lindel¨ofproperty. An L-set having the Lindel¨of property is countably compact if andonly if it is fuzzy compact. ...

In this paper, we prove the following statements: (1) There exists a Tychonoff star countable discrete closed, pseudocompact space having a regular-closed subspace which is not star countable. (2) Every separable space can be embedded into an absolutely star countable discrete closed space as a closed subspace. (3) Assuming 20 = 21 , there exists a normal absolutely star countable discrete clos...

Because the partition coefficient is one of the most important parameters affecting microsegregation, the aim of this research is to experimentally analyse the partition coefficient in Al-Mg alloys. In order to experimentally measure the partition coefficient, a series of quenching experiments during solidification were carried out. For this purpose binary Al-Mg alloys containing 6.7 and 10.2 w...