Related papers: Forcing axioms for $\lambda$-complete $\mu^+$-C.C
Since the seminal work of J. A. Robinson on resolution, many lifting lemmas for simplifying proofs of completeness of resolution have been proposed in the literature. In the logic programming framework, they may also help to detect some…
In this paper we prove a quantitative form of the strong unique continuation property for the Lam\'e system when the Lam\'e coefficients $\mu$ is Lipschitz and $\lambda$ is essentially bounded in dimension $n\ge 2$. This result is an…
We revisit the problem of discriminating orthogonal quantum states within the local quantum operation and classical communication (LOCC) paradigm. Our particular focus is on the asymptotic situation where the parties have infinite resources…
Let B be the Lie algebra with basis {L_{i,j},C|i,j\in Z} and relations [L_{i,j},L_{k,l}]=((j+1)k-i(l+1))L_{i+k,j+l}+i\delta_{i,-k}\delta_{j+l,-2}C, [C,L_{i,j}]=0. It is proved that an irreducible highest weight B-module is quasifinite if…
We study the spectrum of forcing notions between the iterations of $\sigma$-closed followed by ccc forcings and the proper forcings. This includes the hierarchy of $\alpha$-proper forcings for indecomposable countable ordinals as well as…
In this paper, we are concern with the multiplicity of solutions for a p-Laplacian problem. A weaker super-quadratic assumptions is required on the nonlinearity. Under the weaker condition we give a new proof for the infinite solutions…
We use forcing over admissible sets to show that, for every ordinal $\alpha$ in a club $C\subset\omega_1$, there are copies of $\alpha$ such that the isomorphism between them is not computable in the join of the complete $\Pi^1_1$ set…
This note addresses the continuum problem, taking advantage of the breakthrough mentioned in the subtitle, and relating it to many recent advances occurring in set theory.
We present a polymorphic linear lambda-calculus as a proof language for second-order intuitionistic linear logic. The calculus includes addition and scalar multiplication, enabling the proof of a linearity result at the syntactic level.
Labeled examples (i.e., positive and negative examples) are an attractive medium for communicating complex concepts. They are useful for deriving concept expressions (such as in concept learning, interactive concept specification, and…
For a set $\cM=\{-\mu,-\mu+1,\ldots, \lambda\}\setminus\{0\}$ with non-negative integers $\lambda,\mu<q$ not both 0, a subset $\cS$ of the residue class ring $\Z_q$ modulo an integer $q\ge 1$ is called a $(\lambda,\mu;q)$-\emph{covering…
Recent developments in the categorical foundations of universal algebra have given fresh impetus to an understanding of the lambda calculus coming from categorical logic: an interpretation is a semi-closed algebraic theory. Scott's…
In previous works, a tableau calculus has been defined, which constitutes a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work shows how to extend such a calculus to…
Contextuality and nonlocality are non-classical properties exhibited by quantum statistics whose implications profoundly impact both foundations and applications of quantum theory. In this paper we provide some insights into logical…
In this paper we consider Hopf's Lemma and the Strong Maximum Principle for supersolutions to a class of non elliptic equations. In particular we prove a sufficient condition for the validity of Hopf's Lemma and of the Strong Maximum…
We study a family of variants of Jensen's\emph{subcomplete forcing axiom}, $\mathsf{SCFA}$ and \emph{subproper forcing axiom}, $\mathsf{SubPFA}$. Using these we develop a general technique for proving non-implications of $\mathsf{SCFA}$,…
Using an algebraic framework we solve a problem posed in [5] and [7] about the axiomatizability of a quantum computational type logic related to fuzzy logic. A Hilbert-style calculus is developed obtaining an algebraic strong completeness…
We consider the equation $$ ab + cd = \lambda, \qquad a\in A, b \in B, c\in C, d \in D, $$ over a finite field $F_q$ of $q$ elements, with variables from arbitrary sets $ A, B, C, D \subseteq F_q$. The question of solvability of such and…
This is a report on state-of-the-art on the question of developing higher analogues of the forcing axiom PFA. Recently there have been several attempts to develop forcing axioms analogous to the proper forcing axiom (PFA) for cardinals of…
We give a short, self-contained proof of two key results from a paper of four of the authors. The first is a kind of weighted discrete Pr\'ekopa-Leindler inequality. This is then applied to show that if $A, B \subseteq \mathbb{Z}^d$ are…