Related papers: The strength of countable saturation
The production and manipulation of quantum correlation protocols will play a central role where the quantum nature of the correlation can be used as a resource to yield properties unachievable within a classical framework is a very active…
The superposition principle lies at the heart of many non-classical properties of quantum mechanics. Motivated by this, we introduce a rigorous resource theory framework for the quantification of superposition of a finite number of linear…
While there is a well-established notion of what a computable ordinal is, the question which functions on the countable ordinals ought to be computable has received less attention so far. We propose a notion of computability on the space of…
We first partly develop a mathematical notion of stable consistency intended to reflect the actual consistency property of human beings. Then we give a generalization of the first and second G\"odel incompleteness theorem to stably…
How useful is a quantum dynamical operation for quantum information processing? Motivated by this question we investigate several strength measures quantifying the resources intrinsic to a quantum operation. We develop a general theory of…
We present a method for constructing countable models of small theories and apply it to prove theorems on the maximal number of countable non-isomorphic models of linearly ordered theories.
Motivated by the Lyapunov convexity theorem in infinite dimensions, we extend the convexity of the integral of a decomposable set to separable Banach spaces under the strengthened notion of nonatomicity of measure spaces, called…
We study $\varepsilon$-stability in continuous logic. We first consider stability in a model, where we obtain a definability of types result with a better approximation than that in the literature. We also prove forking symmetry for…
In this paper, we study additional aspects of the capacity distribution on the set $\mathcal{B}_n$ of compositions of $n$ consisting of $1$'s and $2$'s. Among our results are further recurrences for this distribution as well as formulas for…
We deal with an iteration theorem of forcing notion with a kind of countable support of nice enough forcing notion which is proper aleph_2-c.c. forcing notions. We then look at some special cases (Q_D 's preceded by random forcing).
Matthes and Uustalu (TCS 327(1-2):155-174, 2004) presented a categorical description of substitution systems capable of capturing syntax involving binding which is independent of whether the syntax is made up from least or greatest fixed…
In this note we give a wellfoundedness proof of a computable notation system for first-order reflection.
This paper develops a new framework, \emph{simultaneous saturation}, designed to quantify the size of sets whose elements are simultaneously large. The framework establishes a correspondence between the magnitude of such sets and a system…
We present a type theory with some proof-irrelevance built into the conversion rule. We argue that this feature is useful when type theory is used as the logical formalism underlying a theorem prover. We also show a close relation with the…
We consider strong expansions of the theory of ordered abelian groups. We show that the assumption of strength has a multitude of desirable consequences for the structure of definable sets in such theories, in particular as relates to…
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…
For a few pairs $G\subset \hat G$ of reductive groups, we study the decomposition of irreducible $\hait G$-modules into $G$-modules. In particular, we observe the saturation property for all of these pairs.
This paper examines a denumerable version of the nested-set theorem and derives from it a contradiction involving the formal consistency of the actual infinity assumed by the Axiom of Infinity.
In this work, we prove the existence of solutions for a tripled system of integral equations using some new results of fixed point theory associated with measure of noncompactness. These results extend some previous works in the literature,…
Recent developments in Quantum Machine Learning have seen the introduction of several models to generalize the classical perceptron to the quantum regime. The capabilities of these quantum models need to be determined precisely in order to…