Proof of the quadratic reciprocity law in primitive recursive arithmetic.
Proof theory for full intuitionistic linear logic, bilinear logic, and MIX categories.
Proper forcings and absoluteness in
We show that in the presence of large cardinals proper forcings do not change the theory of with real and ordinal parameters and do not code any set of ordinals into the reals unless that set has already been so coded in the ground model.
Proper translation
We continue our work on weak diamonds [J. Appl. Anal. 15 (1009)]. We show that together with the weak diamond for covering by thin trees, the weak diamond for covering by meagre sets, the weak diamond for covering by null sets, and “all Aronszajn trees are special” is consistent relative to ZFC. We iterate alternately forcings specialising Aronszajn trees without adding reals (the NNR forcing from [“Proper and Improper Forcing”, Ch. V]) and < ω₁-proper -bounding forcings adding reals. We show...
Properties of extensions of algebraically maximal fields.
We prove some properties similar to the theorem Ax-Kochen-Ershov, in some cases of pairs of algebraically maximal fields of residue characteristic p > 0. This properties hold in particular for pairs of Kaplansky fields of equal characteristic, formally p-adic fields and finitely ramified fields. From that we derive results about decidability of such extensions.
Properties of forcing preserved by finite support iterations
We shall investigate some properties of forcing which are preserved by finite support iterations and which ensure that unbounded families in given partially ordered sets remain unbounded.
Properties of fuzzy relations powers
Properties of - compositions of fuzzy relations were first examined in Goguen [8] and next discussed by many authors. Power sequence of fuzzy relations was mainly considered in the case of matrices of fuzzy relation on a finite set. We consider - powers of fuzzy relations under diverse assumptions about operation. At first, we remind fundamental properties of - composition. Then, we introduce some manipulations on relation powers. Next, the closure and interior of fuzzy relations are examined....
Properties of measure and category in generalized Cohen's and Silver's forcing
Properties of quantum logic maps as fuzzy relations on a set of all symmetric and idempotent binary matrices
A quantum logic is one of possible mathematical models for non-compatible random events. In this work we solve a problem proposed at the conference FSTA 2006. Namely, it is proved that s-maps are symmetric fuzzy relations on a set of all symmetric and idempotent binary matrices. Consequently s-maps are not antisymmetric fuzzy relations. This paper also explores other properties of s-maps, j-maps and d-maps. Specifically, it is proved that s-maps are neither reflexive, nor irreflexive, and nor transitive,...
Properties of the class of measure separable compact spaces
We investigate properties of the class of compact spaces on which every regular Borel measure is separable. This class will be referred to as MS. We discuss some closure properties of MS, and show that some simply defined compact spaces, such as compact ordered spaces or compact scattered spaces, are in MS. Most of the basic theory for regular measures is true just in ZFC. On the other hand, the existence of a compact ordered scattered space which carries a non-separable (non-regular) Borel measure...
Properties of the nearest parametric form approximation operator of fuzzy numbers.
Property C'', strong measure zero sets and subsets of the plane
Let X be a set of reals. We show that • X has property C" of Rothberger iff for all closed F ⊆ ℝ × ℝ with vertical sections (x ∈ X) null, is null; • X has strong measure zero iff for all closed F ⊆ ℝ × ℝ with all vertical sections (x ∈ ℝ) null, is null.
Proposal for a natural formalization of functional programming concepts
Propositional calculus for adjointness lattices.
Propositional calculus proving methods in Prolog
Propositional dynamic logic with recursive programs
Propositional extensions of [Book]
Propositional Linear Temporal Logic with Initial Validity Semantics1
In the article [10] a formal system for Propositional Linear Temporal Logic (in short LTLB) with normal semantics is introduced. The language of this logic consists of “until” operator in a very strict version. The very strict “until” operator enables to express all other temporal operators. In this article we construct a formal system for LTLB with the initial semantics [12]. Initial semantics means that we define the validity of the formula in a model as satisfaction in the initial state of model...
Proprietà metamatematiche di alcune classi di algebre
Propriété de Baire de muni d’une nouvelle topologie et application à la construction d’ultrafiltres