相关论文: Non Cohen Oracle c.c.c

To expand a fundamental theory of context-free languages, we equip nondeterministic one-way pushdown automata with additional oracle mechanisms, which naturally induce various nondeterministic reducibilities among formal languages. As a…

We study the quantum-classical polynomial hierarchy, QCPH, which is the class of languages solvable by a constant number of alternating classical quantifiers followed by a quantum verifier. Our main result is that QCPH is infinite relative…

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).

We develop a correspondence between the theory of sequential algorithms and classical reasoning, via Kreisel's no-counterexample interpretation. Our framework views realizers of the no-counterexample interpretation as dynamic processes…

The aim of this short note is to communicate a simple solution to the problem posed in [1] as Question 7.2.7: is it true that for every ccc $\sigma$-ideal I any I-positive Borel set contains modulo I an I-positive closed set?

The forcing theorem is the most fundamental result about set forcing, stating that the forcing relation for any set forcing is definable and that the truth lemma holds, that is everything that holds in a generic extension is forced by a…

We develop a toolbox for forcing over arbitrary models of set theory without the axiom of choice. In particular, we introduce a variant of the countable chain condition and prove an iteration theorem that applies to many classical forcings…

The tree forcing method given by (Liu 2015) enables the cone avoiding of strong enumeration of a given tree, within a subset or co-subset of an arbitrary given set, provided the given tree does not admit computable strong enumeration. Using…

Chain conditions are one of the major tools used in the theory of forcing. We say that a partial order has the countable chain condition if every antichain (in the sense of forcing) is countable. Without the axiom of choice antichains tend…

We give an example of a regular and complete subalgebra of a Cohen algebra which is not Cohen.

We look for a parallel to the notion of ``proper forcing'' among lambda-complete forcing notions not collapsing lambda^+ . We suggest such a definition and prove that it is preserved by suitable iterations.

Algebras on the natural numbers and their clones of term operations can be classified according to their descriptive complexity. We give an example of a closed algebra which has only unary operations and whose clone of term operations is…

This is an overview about a method of constructing ccc forcings: Suppose first that a continuous, commutative system of complete embeddings between countable forcings indexed along $\omega_1$ is given. Then its direct limit satisfies ccc by…

Pairwise "same-cluster" queries are one of the most widely used forms of supervision in semi-supervised clustering. However, it is impractical to ask human oracles to answer every query correctly. In this paper, we study the influence of…

The random oracle methodology has proven to be a powerful tool for designing and reasoning about cryptographic schemes. In this paper, we focus on the basic problem of correcting faulty or adversarially corrupted random oracles, so that…

We prove that CH implies the existence of a Cohen-indestructible mad family such that the Mathias forcing associated to its filter adds dominating reals, while $\mathfrak b=\mathfrak c$ is consistent with the negation of this statement as…

We prove it consistent relative to ZFC that all nontrivial forcings of size $\aleph _1$ add a Cohen real.

The Quantum Oracle Classification (QOC) problem is to classify a function, given only quantum black box access, into one of several classes without necessarily determining the entire function. Generally, QOC captures a very wide range of…

We study fair clustering problems in a setting where distance information is obtained from two sources: a strong oracle providing exact distances, but at a high cost, and a weak oracle providing potentially inaccurate distance estimates at…

Suppose we are given a computably enumerable object arise from algorithmic randomness or computable analysis. We are interested in the strength of oracles which can compute an object that approximates this c.e. object. It turns out that,…