Questa è la prima parte di una articolo espositivo dedicato ai teoremi di assolutezza, un argomento che sta assumendo un’importanza via via più grande in teoria degli insiemi. In questa prima parte vedremo come le questioni di teoria dei numeri non siano influenzate da assunzioni insiemistiche quali l’assioma di scelta o l’ipotesi del continuo.
Questa è la seconda parte dell’articolo espositivo [A]. Qui vedremo come siapossibile utilizzare il forcinge gli assiomi forti dell’infinito per dimostrare nuovi teoremi sui numeri reali.
We prove that for every Borel ideal, the ideal limits of sequences of continuous functions on a Polish space are of Baire class one if and only if the ideal does not contain a copy of Fin × Fin. In particular, this is true for ideals. In the proof we use Borel determinacy for a game introduced by C. Laflamme.
In recent work we have proposed a novel approach to define idealized type systems for object-oriented languages, based on abstract compilation of programs into Horn formulas which are interpreted w.r.t. the coinductive (that is, the greatest) Herbrand model. In this paper we investigate how this approach can be applied also in the presence of imperative features. This is made possible by considering a natural translation of Static Single Assignment intermediate form programs into Horn formulas,...
In recent work we have proposed a novel approach to define idealized type systems for object-oriented languages, based on abstract compilation of programs into Horn formulas which are interpreted w.r.t. the coinductive (that is, the greatest) Herbrand model. In this paper we investigate how this approach can be applied also in the presence of imperative features. This is made possible by considering a natural translation of Static Single Assignment intermediate form programs into Horn formulas,...
We use Tsirelson’s Banach space ([2]) to define an P-ideal which refutes a conjecture of Mazur and Kechris (see [12, 9, 8]).
Countable products of finite discrete spaces with more than one point and ideals generated by Marczewski-Burstin bases (assigned to trimmed trees) are examined, using machinery of base tree in the sense of B. Balcar and P. Simon. Applying Kulpa-Szymanski Theorem, we prove that the covering number equals to the additivity or the additivity plus for each of the ideals considered.
Given a topological space ⟨X,T⟩ ∈ M, an elementary submodel of set theory, we define to be X ∩ M with topology generated by U ∩ M:U ∈ T ∩ M. We prove that if is homeomorphic to ℝ, then . The same holds for arbitrary locally compact uncountable separable metric spaces, but is independent of ZFC if “local compactness” is omitted.
Characterizations of IF-filters of a pseudo-BL-algebra are established. Some related properties are investigated. The notation of prime IF- filters and a characterization of a pseudo-BL-chain are given. Homomorphisms of IF-filters and direct product of IF-filters are studied.
Ko [26] and Bruschi [11] independently showed that, in some relativized world, PSPACE (in fact, ⊕P) contains a set that is immune to the polynomial hierarchy (PH). In this paper, we study and settle the question of relativized separations with immunity for PH and the counting classes PP, , and ⊕P in all possible pairwise combinations. Our main result is that there is an oracle A relative to which contains a set that is immune BPP⊕P. In particular, this set is immune to PHA and to ⊕PA. Strengthening...
We introduce the concepts of pre-implication algebra and implication algebra based on orthosemilattices which generalize the concepts of implication algebra, orthoimplication algebra defined by J.C. Abbott [2] and orthomodular implication algebra introduced by the author with his collaborators. For our algebras we get new axiom systems compatible with that of an implication algebra. This unified approach enables us to compare the mentioned algebras and apply a unified treatment of congruence properties....
A term operation implication is introduced in a given basic algebra and properties of the implication reduct of are treated. We characterize such implication basic algebras and get congruence properties of the variety of these algebras. A term operation equivalence is introduced later and properties of this operation are described. It is shown how this operation is related with the induced partial order of and, if this partial order is linear, the algebra can be reconstructed by means of...