Related papers: The grounded Martin's axiom
In this paper we consider propositional calculi, which are finitely axiomatizable extensions of intuitionistic implicational propositional calculus together with the rules of modus ponens and substitution. We give a proof of undecidability…
In this paper we consider the Foreman's maximality principle, which says that any non-trivial forcing notion either adds a new real or collapses some cardinals. We prove the consistency of some of its consequences. We prove that it is…
We offer a view of mathematics as an experimental science where axioms play the role of foundational theories like general relativity and quantum mechanics in physics. Under this view, axioms are provisional and inferred from experience…
We prove the following theorem: For a partially ordered set Q such that every countable subset has a strict upper bound, there is a forcing notion satisfying ccc such that, in the forcing model, there is a basis of the meager ideal of the…
Aspects of parity-preserving, three-dimensional conformal field theories (CFTs) with a global $U(1)$ symmetry in the presence of a background magnetic field are investigated. A local effective action is constructed to four-derivative order,…
Our original aim was, in Abelian group theory to prove the consistency of: lambda is strong limit singular and for some properties of abelian groups which are relatives of being free, the compactness in singular fails. In fact this should…
We note that some form of the condition "$p_1, p_2$ have a $\leq_{\mathbb{Q}}$-lub in $\mathbb{Q}$" is necessary in some forcing axiom for $\lambda$-complete $\mu^+$-c.c. forcing notions. We also show some versions are really stronger than…
It was argued [1] that there can be no extension of quantum mechanics with improved predictive power on a measurement freely chosen, independently of any event that is not in its future light cone. The assumption of measurement choice was…
A gravitational theory with derivative matter coupling is proposed which adopt de Sitter expansion at late times with ordinary baryonic matter. Matter components are conserved separately in the cosmological background and the Newtonian…
We prove forcing axiom equivalents of two families of weakenings of the axiom of choice: a trichotomy principle for cardinals isolated by L\'evy, ${\rm H\hskip0.05pt}_\kappa$, and ${\rm DC}_\kappa$, the principle of dependent choices…
We present different extensions of the Banach contraction principle in the $G$-metric space setting. More precisely, we consider mappings for which the contractive condition is satisfied by a power of the mapping and for which the power…
After surveying classical results, we introduce a generalized notion of inference system to support structural recursion on non-well-founded data types. Besides axioms and inference rules with the usual meaning, a generalized inference…
A diagonal version of the strong reflection principle is introduced, along with fragments of this principle associated to arbitrary forcing classes. The relationships between the resulting principles and related principles, such as the…
Quantum mechanics is an extremely successful theory of nature and yet it lacks an intuitive axiomatization. In contrast, the special theory of relativity is well understood and is rooted into natural or experimentally justified postulates.…
David Aspero asks on the possibility of having Forcing axiom FA_{aleph_2}(K), where K is the class of forcing notions preserving stationarity of subsets of aleph_1 and of aleph_2. We answer negatively, in fact we show the negative result…
Chern-Simons modified gravity is an effective extension of general relativity that captures leading-order, gravitational parity violation. Such an effective theory is motivated by anomaly cancelation in particle physics and string theory.…
We investigate the existence and the properties of fully separable (fully factorized) ground states in quantum spin systems. Exploiting techniques of quantum information and entanglement theory we extend a recently introduced method and…
We show that Dependent Choice is a sufficient choice principle for developing the basic theory of proper forcing, and for deriving generic absoluteness for the Chang model in the presence of large cardinals, even with respect to…
The paper discusses the problem of the Lorentz contraction in accelerated systems, in the context of the special theory of relativity. Equal proper accelerations along different world lines are considered, showing the differences arising…
We extend the usual gravitational action principle by promoting the bare cosmological constant (CC) from a parameter to a field which can take many possible values. Variation leads to a new integral constraint equation which determines the…