‎for a set of non-negative integers~$l$‎, ‎the $l$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $a_v subseteq {1,dots‎, ‎l}$ to vertices $v$‎, ‎such that every two vertices $u,v$ are adjacent if and only if $|a_u cap a_v|in l$‎. ‎the bipartite $l$-intersection number is defined similarly when the conditions are considered only for the ver...

Abstract Background: Identity disturbance is one of the DSM-IV criteria for borderline personality disorder, but there has been little attention to its nature. Four subsets of identity disturbance (role absorption, painful incoherence, inconsistency and lack of commitment) have been assessed. This study aimed to assess the role of these subsets in patients with borderline person...

‎For a set of non-negative integers~$L$‎, ‎the $L$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $A_v subseteq {1,dots‎, ‎l}$ to vertices $v$‎, ‎such that every two vertices $u,v$ are adjacent if and only if $|A_u cap A_v|in L$‎. ‎The bipartite $L$-intersection number is defined similarly when the conditions are considered only for the ver...

We compare the monadic second-order theory of an arbitrary linear ordering L with the theory of the family of subsets of L endowed with the operation on subsets obtained by lifting the max operation on L. We show that the two theories define the same relations. The same result holds when lifting the min operation or both max and min operations.

Crisp and L-fuzzy ambiguous representations of closed subsets of one space by closed subsets of another space are introduced. It is shown that, for each pair of compact Hausdorff spaces, the set of (crisp or L-fuzzy) ambiguous representations is a lattice and a compact Hausdorff Lawson upper semilattice. The categories of ambiguous and L-ambiguous representations are defined and investigated.

We call a subset of an ordinal λ recognizable if it is the unique subset x of λ for which some Turing machine with ordinal time and tape, which halts for all subsets of λ as input, halts with the final state 0. Equivalently, such a set is the unique subset x which satisfies a given Σ1 formula in L[x]. We prove several results about sets of ordinals recognizable from ordinal parameters by ordina...

We call a subset of an ordinal recognizable if it is the unique subset x of for which some Turing machine with ordinal time and tape and an ordinal parameter, that halts for all subsets of as input, halts with the final state 0. Equivalently, such a set is the unique subset x which satisfies a given ⌃1 formula in L[x]. We further define the recognizable closure for subsets of by closing under r...

A theorem of Sperner [2] states that a collection of subsets of (l,..., n), no two ordered by inclusion, contains at most ( &,) sets. How many twoelement chains A cB of subsets of {I,..., n} can be found such that sets in different chains are not related? More generally, we seek to determinef,(n), defined to be the maximum m such that there exist subsets A(i,j) 5 {l,..., n}, 1 < i < m, 0 <j < k...