相关论文: TD implies CCR

It is well known that in Zermelo-Fraenkel (ZF) set theory any finite set is decidable. In this paper we discuss an extension of ZF where this result is no longer valid. Such an extension is quasi-set theory and it has its origin on problems…

Generalised Probabilistic Theories (GPTs) provide a unifying framework encompassing classical theories, quantum theories, as well as hypothetical alternatives. We investigate the problem of extending a system with a finite set of…

We prove, assuming resolution of singularities in positive characteristic, an analogue of Siegel's theorem on sum of squares in positive characteristic. The method of proof combines techniques from central simple algebras with model theory…

We show that Morley's theorem on the number of countable models of a countable first-order theory becomes an undecidable statement when extended to second-order logic. More generally, we calculate the number of equivalence classes of…

We present a method to prove the decidability of provability in several well-known inference systems. This method generalizes both cut-elimination and the construction of an automaton recognizing the provable propositions.

$AD_{\mathbb{R}}$ is the Axiom of Determinacy for games on the reals (i.e., the player play reals. We show that it implies that all sets of reals are Theta-universally Baire. As a corollary we obtain a model in which $AD$ holds and all sets…

We study a well-known technique of using absoluteness for giving choice-free proofs to some statements which are known to be provable with the axiom of choice. The idea is to reduce the problem to an inner model where the axiom of choice…

It is well known that ZFC, despite its usefulness as a foundational theory for mathematics, has two unwanted features: it cannot be written down explicitly due to its infinitely many axioms, and it has a countable model due to the…

We characterize countable dimensionality and strong countable dimensionality by means of an infinite game.

We prove axiomatic characterizations of several important multiwinner rules within the class of approval-based committee choice rules. These are voting rules that return a set of (fixed-size) committees. In particular, we provide axiomatic…

The multiplicative theory of a set of numbers (which could be natural, integer, rational, real or complex numbers) is the first-order theory of the structure of that set with (solely) the multiplication operation (that set is taken to be…

Let $T$ be a theory. If $T$ eliminates $\exists^\infty$, it need not follow that $T^{eq}$ eliminates $\exists^\infty$, as shown by the example of the $p$-adics. We give a criterion to determine whether $T^{eq}$ eliminates $\exists^\infty$.…

A folk theorem says higher order arithmetic has the proof theoretic strength of set theory with limited power set. This paper makes the theorem precise in terms of several axiom system based on ZF.

Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html ) is a research program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth which it has more traditionally been.…

We provide a simple proof of a computable analogue to the Jayne Rogers Theorem from descriptive set theory. The difficulty of the proof is delegated to a simulation result pertaining to non-deterministic type-2 machines. Thus, we…

The well known Andrews-Curtis Conjecture [2] is still open. In this paper, we establish its finite version by describing precisely the connected components of the Andrews-Curtis graphs of finite groups. This finite version has independent…

One of the fundamental results in computability is the existence of well-defined functions that cannot be computed. In this paper we study the effects of data representation on computability; we show that, while for each possible way of…

In this paper, we modify some previous definitions of fuzzy Turing machines to define the notions of accepting and rejecting degrees of inputs, computationally. We use a BFS-based search method and obtain an upper level bound to guarantee…

Query determinacy is decidable for project-select views and a project-select-join query with no self joins, as long as the selection predicates are in a first-order theory for which satisfiability is decidable.

In this paper, we interpret NDTM (NonDeterministic Turing Machine) used to define NP by tracing to the source of NP. Originally NP was defined as the class of problems solvable in polynomial time by a NDTM in the theorem of Cook, where the…