Miloš S. Kurilić

A family of strict and discontinuous triangular norms

Answers to some questions about triangular norms are given. Precisely, a procedure of construction of infinitely many triangular norms is obtained (one for each operation ∗ : N2 → N such that 〈N <, ∗〉 is a strictly ordered commutative semigroup). Each of them is discontinuous at each point of a dense subset of [0, 1]2 and it satisfies the condition T(kx, y) = T(x,ky) for infinitely many k ϵ [0, 1].

Forcing by non-scattered sets

Abstract We show that for each non-scattered linear order 〈 L , 〉 the set of non-scattered subsets of L ordered by the inclusion is forcing equivalent to the two-step iteration of the Sacks forcing and a σ -closed forcing. If the equality sh ( S ) = ℵ 1 or PFA holds in the ground model, then the second iterand is forcing equivalent to the algebra P ( ω ) / Fin of the Sacks extension.

Posets of copies of countable scattered linear orders

Abstract We show that the separative quotient of the poset 〈 P ( L ) , ⊂ 〉 of isomorphic suborders of a countable scattered linear order L is σ -closed and atomless. So, under the CH, all these posets are forcing-equivalent (to ( P ( ω ) / Fin ) + ).

FROM A 1 TO D 5 : TOWARDS A FORCING-RELATED CLASSIFICATION OF RELATIONAL STRUCTURES

We investigate the partial orderings of the form (P(X),\subset), where X is a relational structure and P(X) the set of the domains of its isomorphic substructures. A rough classification of countable binary structures corresponding to the forcing-related properties of the posets of their copies is obtained.

Maximally embeddable components

We investigate the partial orderings of the form

Different similarities

{\langle \mathbb{P}(\mathbb{X}), \subset \rangle}

Independence of Boolean algebras and forcing

〈P(X),⊂〉 , where