In the proof of the consistency of the Continuum Hypothesis and the Axiom of Choice with the other axioms of set theory, Gödel [ l ] introduced the notion of a constructible set and showed that the constructible sets form a model for set theory. These sets are intuitively those which can be reached by means of a transfinite sequence of several simple operations. He then showed that the Axiom of...

ion_map(BindMapDefn) --> bindings_map_definition(BindMapDefn). abstraction_map(Omd) --> other_map_definition(Omd). abstraction_map([]) --> []. property_s_list([Prop|PropL]) --> property_s(Prop), [token(’;’, misc)], property_s_list(PropL). property_s_list([Prop]) --> property_s(Prop), opt_semi. property_s_list([]) --> []. bindings_map_definition(bindings_map_definition(TypedId, BindL)) --> [toke...

in this paper, the notion of maximal m-open set is introduced and itsproperties are investigated. some results about existence of maximal m-open setsare given. moreover, the relations between maximal m-open sets in an m-spaceand maximal open sets in the corresponding generated topology are considered.our results are supported by examples and counterexamples.

‎let $x=left(‎ ‎begin{array}{llll}‎ ‎ x_1 & ldots & x_{n-1}& x_n‎ ‎ x_2& ldots & x_n & x_{n+1}‎ ‎end{array}right)$ be the hankel matrix of size $2times n$ and let $g$ be a closed graph on the vertex set $[n].$ we study the binomial ideal $i_gsubset k[x_1,ldots,x_{n+1}]$ which is generated by all the $2$-minors of $x$ which correspond to the edges of $g.$ we show that...

let $l$ be a completely regular frame and $mathcal{r}l$ be the ringof continuous real-valued functions on $l$. we study the frame$mathfrak{o}(min(mathcal{r}l))$ of minimal prime ideals of$mathcal{r}l$ in relation to $beta l$. for $iinbeta l$, denoteby $textit{textbf{o}}^i$ the ideal${alphainmathcal{r}lmidcozalphain i}$ of $mathcal{r}l$. weshow that sending $i$ to the set of minimal prime ideals...